- 6.1: The Central Limit Theorem for Sums
- The central limit theorem tells us that for a population with any distribution, the distribution of the sums for the sample means approaches a normal distribution as the sample size increases. In other words, if the sample size is large enough, the distribution of the sums can be approximated by a normal distribution even if the original population is not normally distributed.

- 6.2: A Single Population Mean using the Student t-Distribution
- We rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation ss as an estimate for σσ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.

## 6: Estimating Averages

A manager of a warehouse wants to know how much a typical supplier delivers in 1000 dollar units. He/she takes a sample of 12 suppliers, at random, obtaining the following results:

Supplier | Amount | Supplier | Amount |
---|---|---|---|

1 | 9 | 7 | 11 |

2 | 8 | 8 | 7 |

3 | 9 | 9 | 13 |

4 | 12 | 10 | 9 |

5 | 9 | 11 | 11 |

6 | 12 | 12 | 10 |

*expenditure of a typical supplier.*

- The "error" = true amount spent minus the estimated amount.
- The "error squared" is the error above, squared.
- The "SSE" is the sum of the squared errors.
- The "MSE" is the mean of the squared errors.

Supplier | $ | Error | Error Squared |
---|---|---|---|

1 | 9 | -1 | 1 |

2 | 8 | -2 | 4 |

3 | 9 | -1 | 1 |

4 | 12 | 2 | 4 |

5 | 9 | -1 | 1 |

6 | 12 | 2 | 4 |

7 | 11 | 1 | 1 |

8 | 7 | -3 | 9 |

9 | 13 | 3 | 9 |

10 | 9 | -1 | 1 |

11 | 11 | 1 | 1 |

12 | 10 | 0 | 0 |

The SSE = 36 and the MSE = 36/12 = 3. Table of MSE results for example using different estimates So how good was the estimator for the amount spent for each supplier? Let us compare the estimate (10) with the following estimates: 7, 9, and 12. That is, we estimate that each supplier will spend $7, or $9 or $12.

Performing the same calculations we arrive at:

Estimator | 7 | 9 | 10 | 12 |
---|---|---|---|---|

SSE | 144 | 48 | 36 | 84 |

MSE | 12 | 4 | 3 | 7 |

The estimator with the smallest MSE is the best. It can be shown mathematically that the estimator that minimizes the MSE for a set of random data is the mean. Table showing squared error for the mean for sample data Next we will examine the mean to see how well it predicts net income over time.

The next table gives the income before taxes of a PC manufacturer between 1985 and 1994.

Year | $ (millions) | Mean | Error | Squared Error |
---|---|---|---|---|

1985 | 46.163 | 48.676 | -2.513 | 6.313 |

1986 | 46.998 | 48.676 | -1.678 | 2.814 |

1987 | 47.816 | 48.676 | -0.860 | 0.739 |

1988 | 48.311 | 48.676 | -0.365 | 0.133 |

1989 | 48.758 | 48.676 | 0.082 | 0.007 |

1990 | 49.164 | 48.676 | 0.488 | 0.239 |

1991 | 49.548 | 48.676 | 0.872 | 0.761 |

1992 | 48.915 | 48.676 | 0.239 | 0.057 |

1993 | 50.315 | 48.676 | 1.639 | 2.688 |

1994 | 50.768 | 48.676 | 2.092 | 4.378 |

- The "simple" average or mean of all past observations is only a useful estimate for forecasting when there are no trends. If there are trends, use different estimates that take the trend into account.

The multiplier 1/3 is called the *weight*. In general:

$ ar *^ *

## 6.2 Original Reservoir Pressure in Infinite Reservoirs

Original reservoir pressure, *p _{i}* is found as suggested by ideal theory. We simply identify the middle-time line, extrapolate it to infinite shut-in time, and read the pressure that is the original reservoir pressure as shown in Figure 6-1.

This technique is possible only for a well in a new reservoir, i.e., one in which there has been negligible pressure depletion. For a reservoir with one or more boundaries relatively near a tested well, the late-time line must be extrapolated to find *p _{i}* (Figure 6-2).

Figure 6-1: Buildup test graph for infinite-acting reservoir />

Figure 6-2: Buildup test graph for well near reservoir limit

## Important facts about word problems solving and estimation for Grade 6

In a significant way, our super amazing problem solving and estimation worksheets will help your young math learners to quickly understand the relevance of estimation skills in math concepts and real life.

It should be noted that, not only are these problem solving and estimation skills a key part in math concepts, but are equally an important approach to boast your kid&rsquos mental math skills, logical and creative thinking abilities.

### How can estimation skills enhance kid&rsquos accuracy and experts in math?

If your kids can vividly estimate reasonably, then there&rsquoll be no doubt that their accuracy in math will increase, thus math experts.

Moreover, with estimation skills, they can quickly determine whether their answer is within a reasonable range or not.

Given that estimation skill enhances kid&rsquos mental math competency, your 6 th grader will be able to arrive at reasonable or concrete answers within a twinkle of an eye.

Most importantly, these problem solving and estimation skills will not only strengthen kid&rsquos skills on basic math operations, but will prepare them for areas of advanced math, such as probability, statistics, geometry and algebra. At this point, they will be required to apply logical reasoning and estimation skills.

### How is estimation skill relevant in our daily lives?

Whether at home, in the market, on the street or among friends, our activities will always be surrounded around estimation. This is true as we keep on using the phrase &ldquoLet&rsquos say&hellip&hellip.&rdquo.

So, problem solving and estimation skills will help your kids to easily

- Estimate recipes when cooking, baking, etc.
- Estimate the cost of items in a grocery store, i.e. if you want to stay within a budget
- Estimate the number of people you&rsquoll invite for your coming event, depending on the budget available.
- Estimate and know how to manage or spend your precious time. This will prevent careless distractions and as well encourage you to accomplish your task.

### Vital strategies, best for solving estimation word problems for 6 th grade

Our grade 6 math word problem worksheets with answers are a perfect example for kids to grab * vital strategies, best for solving estimation word problems for 6 th grade*.

What then are those peculiar strategies to consider when faced with situations of problem solving and estimation?

Most at times, math word problems require a __step-by-step__ solving procedure. This is relevant to our multi steps word problems exercise. But before we begin solving these word problems, we need to

- Carefully read the entire problem, twice, in order to better understand its key words.
- Having understood the problem well, endeavor to estimate the answer before solving.
- When solving, show a step-by-step calculation, making visible diverse operation signs where necessary.

Finally, check the reasonableness of your answer by comparing it with the one you estimated above.

## Estimating the number of quit attempts it takes to quit smoking successfully in a longitudinal cohort of smokers

**Objectives:** The number of quit attempts it takes a smoker to quit successfully is a commonly reported figure among smoking cessation programmes, but previous estimates have been based on lifetime recall in cross-sectional samples of successful quitters only. The purpose of this study is to improve the estimate of number of quit attempts prior to quitting successfully.

**Design:** We used data from 1277 participants who had made an attempt to quit smoking in the Ontario Tobacco Survey, a longitudinal survey of smokers followed every 6 months for up to 3 years beginning in 2005. We calculated the number of quit attempts prior to quitting successfully under four different sets of assumptions. Our expected best set of assumptions incorporated a life table approach accounting for the declining success rates for subsequent observed quit attempts in the cohort.

**Results:** The estimated average number of quit attempts expected before quitting successfully ranged from 6.1 under the assumptions consistent with prior research, 19.6 using a constant rate approach, 29.6 using the method with the expected lowest bias, to 142 using an approach including previous recall history.

**Conclusions:** Previous estimates of number of quit attempts required to quit may be underestimating the average number of attempts as these estimates excluded smokers who have greater difficulty quitting and relied on lifetime recall of number of attempts. Understanding that for many smokers it may take 30 or more quit attempts before being successful may assist with clinical expectations.

**Keywords:** addiction longitudinal population smoking cessation.

## 6: Estimating Averages

This section looks at averages.

There are three main types of average:

**mean**- The mean is what most people mean when they say 'average'. It is found by adding up all of the numbers you have to find the mean of, and dividing by the number of numbers. So the mean of 3, 5, 7, 3 and 5 is 23/5 = 4.6 .**mode -**The mode is the number in a set of numbers which occurs the most. So the modal value of 5, 6, 3, 4, 5, 2, 5 and 3 is 5, because there are more 5s than any other number.**median**- The median of a group of numbers is the number in the middle, when the numbers are in order of magnitude. For example, if the set of numbers is 4, 1, 6, 2, 6, 7, 8, the median is 6

This video shows you how to calculate the mean, median and mode

When you are given data which has been grouped, you can't work out the mean exactly because you don't know what the values are exactly (you just know that they are between certain values). However, we calculate an estimate of the mean with the formula: ∑fx / ∑f , where f is the frequency and x is the midpoint of the group (∑ means 'the sum of').

Work out an estimate for the mean height, when the heights of 23 people are given by the first two columns of this table:

Height (cm) | Number of People (f) | Midpoint (x) | fx |

101-120 | 1 | 110.5 | 110.5 |

121-130 | 3 | 125.5 | 376.5 |

131-140 | 5 | 135.5 | 677.5 |

141-150 | 7 | 145.5 | 1018.5 |

151-160 | 4 | 155.5 | 622 |

161-170 | 2 | 165.5 | 331 |

171-190 | 1 | 180.5 | 180.5 |

In this example, the data is grouped. You couldn't find the mean the "normal way" (by adding up the numbers and dividing by the number of numbers) because you don't know what the values are. You know that three people have heights between 121 and 130cm, for example, but you don't know what the heights are exactly. So we estimate the mean, using "∑fx / ∑f".

A good way of setting out your answer would be to add two columns to the table, as I have.

"Midpoint" means the midpoint of each of the groups. So the first entry is the middle of the group 101-120 = 110.5 .

Now,

∑fx (add up all of the values in the last column) = 3316.5

∑f = 23

So an estimate of the mean is 3316.5/23 = __144cm__ (3s.f.)

This short video shows you how to find the mean, mode and median from a frequency table for both discrete and grouped data.

A moving average is used to compare a set of figures over time. For example, suppose you have measured the weight of a child over an eight year period and have the following figures (in kg):

32, 33 ,35, 38, 43, 53, 63 ,65

Taking the mean doesn't give us much useful information. However, we could take the average of each 3 year period. These are the 3-year moving averages.

The first is: (32 + 33 + 35)/3 = 33.3

The second is: (33 + 35 + 38)/3 = 35.3

The third is: (35 + 38 + 43)/3 = 38.7, and so on (there are 3 more!).

To calculate the 4 year moving averages, you'd do 4 years at a time instead, and so on.

The mode is the number in a set of numbers which occurs the most. So the modal value of 5, 6, 3, 4, 5, 2, 5 and 3 is 5, because there are more 5s than any other number.

The range is the largest number in a set minus the smallest number. So the range of 5, 7, 9 and 14 is (14 - 5) = 9. The range gives you an idea of how spread out the data is.

The median of a group of numbers is the number in the middle, when the numbers are in order of magnitude. For example, if the set of numbers is 4, 1, 6, 2, 6, 7, 8, the median is 6:

1, 2, 4, **6**, 6, 7, 8 (6 is the middle value when the numbers are in order)

If you have n numbers in a group, the median is the (n + 1)/2 th value. For example, there are 7 numbers in the example above, so replace n by 7 and the median is the (7 + 1)/2 th value = 4th value. The 4th value is 6.

Many studies have shown that HbA1c is an index of average glucose (AG) over the preceding weeks-to-months. Erythrocyte (red blood cell) life-span averages about 120 days. The level of HbA1c at any point in time is contributed to by all circulating erythrocytes, from the oldest (120 days old) to the youngest. However, HbA1c is a "weighted" average of blood glucose levels during the preceding 120 days, meaning that glucose levels in the preceding 30 days contribute substantially more to the level of HbA1c than do glucose levels 90-120 days earlier. This explains why the level of HbA1c can increase or decrease relatively quickly with large changes in glucose it does not take 120 days to detect a clinically meaningful change in HbA1c following a clinically significant change in AG.

In the Diabetes Control and Complications Trial or DCCT (New Engl J Med 1993329:977-986) study of patients with Type 1 diabetes, quarterly HbA1c determinations were the principal measure of glycemic control study subjects also performed quarterly 24-hour, 7-point capillary-blood glucose profiles. Blood specimens were obtained by subjects in the home setting, pre-meal, 90 minutes post-meal, and at bed-time. In an analysis of the DCCT glucose profile data (Diabetes Care 25:275-278, 2002), mean HbA1c and AG were calculated for each study subject (n= 1439). Results showed a linear relationship between HbA1c and AG (*AG(mg/dL) = ( 35.6 x HbA1c ) - 77.3)*, with a Pearson correlation coefficient (r) of 0.82.

**Data from the A1c-Derived Average Glucose (ADAG) Study:**

A more recent study (2006-2008) sponsored by the ADA, EASD and IDF was designed to better define the mathematical relationship between HbA1c and AG. The study included 507 subjects with Type 1 and Type 2 diabetes and without diabetes from 10 international centers. Estimated AG (eAG) was calculated by combining weighted results from at least 2 days of continuous glucose monitoring performed four times, with seven-point daily self-monitoring of capillary glucose performed at least 3 days per week. The relationship between eAG and HbA1c based on linear regression analysis was:* eAG(mg/dl)= (28.7*HbA1c)-46.7, r2=0.84* (Diabetes Care 200831:1-6). Table 1 depicts this relationship.

More information about eAG, including a calculator to covert eAG to HbA1c and vice-versa, can be found here.

The regression equation from the ADAG study provides lower eAG values compared with the widely used equation derived from the DCCT, and the scatter around the regression is less wide. The proposed explanation for the difference is in the frequency of glucose measurements used to calculate AG, with the ADAG estimate providing a more complete and representative measure of average glucose.

## Estimate your monthly data usage

Use the sliders below to estimate how much usage, on average, your monthly Internet activities take. Or click a data amount on the bar on the right to see a preset data package.

Activity | Data Size |

1 email (no attachments) | 20KB |

1 email (with standard attachments) | 300KB |

1 min. of surfing the web | 250KB(15MB/hr.) |

1 song downloaded | 4MB |

1 photo upload to social media | 5MB |

1 min. of streaming standard-definition video | 11.7MB (700MB/hr.) |

1 min. of streaming high-definition video | 41.7MB (2500MB/hr.) |

1 min. of streaming 4K video | 97.5MB (5850MB/hr.) |

1 min. of online games | 200KB (12MB/hr.) |

**1MB = 1,000KB** approximately**1GB = 1,000MB** approximately**1TB = 1,000GB** approximately

The average cost of car insurance is $1,483 per year. That puts the average car insurance cost per month at $124.

Auto insurance quotes vary widely based on individual rating factors. The Zebra's team of licensed insurance experts crunched the numbers using a composite user profile and gathered rates from the top auto insurance companies to develop these figures. Dive into the data below to see how age, gender, location and vehicle affect auto insurance premiums.

Here at The Zebra, we make it easy for you to find the right coverage—at the right price. We compare top companies so you can find what works for you.

#### Find discounts

#### Understand coverage options

#### Add more drivers or vehicles

Understand coverage options

Add more drivers or vehicles

##### Table of contents:

*Note: All of the insurance resources published by The Zebra are written and reviewed by licensed insurance experts.* *Learn more about The Zebra.*

### Which car insurance companies are the most affordable?

As part of our car insurance rate analysis, we compared premiums from some of America's most popular insurers. Check out average car insurance rates from the best car insurance companies below. Keep in mind your rates will vary, depending on your driving history.

Insurance Company | 6-Month Premium | Monthly Premium |

Allstate | $1,019 | $170 |

Farmers | $788 | $131 |

GEICO | $562 | $94 |

Liberty Mutual | $863 | $144 |

Nationwide | $541 | $90 |

Progressive | $627 | $104 |

State Farm | $646 | $108 |

USAA | $636 | $106 |

Among the surveyed car insurance companies, Nationwide was the cheapest based on our average profile. GEICO came in as second-cheapest. Our individual profile might not reflect your rates, but you can use our auto insurance premiums as a jumping-off point to explore options from multiple car insurance companies.

### Average car insurance rate by coverage level

Depending on your level of coverage, your premium will vary. The average auto insurance policy includes liability insurance with limits of $50,000/$100,000 for bodily injury and $50,000 for property damage coverage, alongside collision and comprehensive deductibles at $500. If you're leasing or financing your vehicle, you might be required to carry gap insurance as well.

We grouped coverage levels by categories of best, good, and minimum, along with average rates for a six-month policy by top insurance companies. See more details per coverage tier:

**Best:**Liability limits of 100/300/100, $500 deductible for collision and comprehensive coverage (full coverage)**Good:**Liability limits of 50/100/50, $1,000 deductible for collision and comprehensive coverage (full coverage)**Minimum:**State minimum liability only, no comprehensive and collision coverage

At every coverage level, Nationwide was the cheapest insurance company but GEICO was not very far behind. Continue reading below to see a breakdown of average premiums for each coverage tier.

#### Average premiums for "best" full coverage car insurance coverage level

We recommend carrying full coverage if you have assets to protect, multiple drivers on your policy (especially teenagers), drive a high-performance or luxury car, or are currently leasing or financing a vehicle. Due to the high liability limits and physical protection provided for your own car at this coverage level, it's typically the most expensive.

Insurance Company | 6-Month Premium | Monthly Premium |

Allstate | $1,070 | $178 |

Farmers | $823 | $137 |

GEICO | $611 | $102 |

Liberty Mutual | $900 | $150 |

Nationwide | $569 | $95 |

Progressive | $673 | $112 |

State Farm | $690 | $115 |

USAA | $672 | $112 |

Not carrying enough liability coverage can leave you at risk of being sued if you cause enough damage to eclipse your liability limits — leaving any assets vulnerable. A $500 deductible is the most common, but you can further decrease your premium by upping your deductible because of the inverse relationship they share — see this illustrated below at the "good" coverage level with a $1,000 deductible.

#### Average premiums for "good" full coverage car insurance coverage level

We generally recommend keeping your liability limits to at least 50/100/50. This middle-of-the-road level of full coverage also provides comprehensive and collision coverage for your own vehicle with a $1,000 deductible.

Insurance Company | 6-Month Premium | Monthly Premium |

Allstate | $877 | $146 |

Farmers | $687 | $115 |

GEICO | $503 | $84 |

Liberty Mutual | $767 | $128 |

Nationwide | $479 | $80 |

Progressive | $553 | $92 |

State Farm | $595 | $99 |

USAA | $555 | $92 |

While a $500 deductible is the most common, you can further decrease your premium with a higher, $1,000 deductible because of the inverse relationship they share. Learn more about how to choose a deductible.

#### Average premiums for "minimum" liability-only car insurance coverage level

Liability limits are set by each state. You must carry at least the state-mandated minimum level of liability insurance in order to be a legal driver in that state. However, keep in mind that this does expose you to more risks:

- A history of having just the minimum level of coverage can reflect negatively on you as a driver in the eyes of an insurance company. They could charge you higher rates because insurers view drivers who consistently carry the minimum amount of insurance as riskier clients.
- In the event of an at-fault accident in which your liability limits aren't sufficient to cover the other driver's injuries and/or property damage, you would be underinsured. You could then be sued to cover the remaining amount.
- If your own vehicle is damaged in an at-fault accident by an uninsured driver or by a comprehensive claim incident (like theft, weather and animal-related damage), you would have no coverage.

Opting for minimum coverage — without comprehensive and collision to cover damage to your own vehicle — is the cheapest tier of auto insurance you can buy.

Insurance Company | 6-Month Premium | Monthly Premium |

Allstate | $378 | $63 |

Farmers | $285 | $47 |

GEICO | $232 | $39 |

Liberty Mutual | $315 | $53 |

Nationwide | $223 | $37 |

Progressive | $258 | $43 |

State Farm | $250 | $42 |

USAA | $233 | $39 |

The less coverage you have, the less your premium will cost. However, it's generally recommended to keep your liability coverage as high as possible to ensure your assets are protected. If your vehicle has any considerable value or you're thinking of selling it in the future, make sure you add comprehensive and collision coverage.

#### Compare rates and find an affordable policy today.

### Average car insurance rates by driver age

Age is a major component of auto insurance premiums. Based on traffic safety data, age is a reliable proxy for risk behind the wheel. To help offset the effect of age on auto insurance and find the cheapest possible rates, we recommend comparing car insurance quotes yearly.

See below the relationship between age and car insurance rates.

Age Group | 6-Month Premium | Monthly Premium |

16-19 | $2,286 | $381 |

20-29 | $943 | $157 |

30-39 | $724 | $121 |

40-49 | $697 | $116 |

50-59 | $649 | $108 |

60-69 | $658 | $110 |

70-79 | $762 | $127 |

80-85 | $882 | $147 |

Those aged 50 to 59 pay the least for car insurance, with all other variables constant. Teen drivers pay the most — about $381 per month for drivers between 16 and 19 years old. Once you turn 20, you should expect an average monthly drop in your insurance premium by about $224.

Aside from very young and very old drivers, age doesn't have a major impact on the average cost of auto insurance. Between the ages of 40 and 60, the average difference in premium is only $45. It's important to consider other rating factors that could have a larger impact on premiums.

### Average car insurance premium by driving record

Getting any type of violation — even a minor one — can have major impacts on your premium. For an at-fault accident, the average rate increase in the last year was $335 per six-month policy — or $670 per year. Most insurance providers will raise rates for three to five years after any violation, ticket or claim.

### Average cost of car insurance by credit score

In all but a handful of states (California, Massachusetts and Hawaii are exceptions), your credit score is a major rating factor. According to the Federal Trade Commission (FTC), drivers with low credit not only file more claims than drivers with high credit but their claims tend to be more expensive. On average, drivers with excellent credit pay $783 less for car insurance than drivers with very poor credit — with all other rating factors constant.

Credit Tier | 6-Month Premium | Monthly Premium |

Very Poor (300-579) | $1,424 | $237 |

Fair (580-669) | $1,127 | $188 |

Good (670-739) | $930 | $155 |

Very Good (740-799) | $779 | $130 |

Exceptional (800-850) | $641 | $107 |

For more information on how your credit score impacts your rates, including car insurance company-specific rates, see our related content below:

#### Compare auto insurance rates today.

### Car insurance rates by gender

In states like California, Hawaii, Massachusetts, Pennsylvania, North Carolina, and Montana, there is no difference in car insurance premiums for men and women. In other states, the difference between car insurance rates for men and women is small — less than a 0.5% difference in car insurance premiums, nationwide.

###### AVERAGE CAR INSURANCE PREMIUMS BY GENDER

Although many people assume car insurance costs vary greatly between men and women, it's a minor factor when you look at the bigger picture. However, gender *does* play a factor in premiums for young drivers. On average, male drivers between the ages of 16 and 19 pay $672 more per year than do female teens.

### Car insurance quote pricing by location

Anytime you move, you'll need to update your car insurance. Car insurance is regulated at the state level and priced by ZIP code. Your exact location can have a major impact on your premium. Compare your rates against your state's average to see whether you're paying too much for auto insurance.

State | Average 6-Month Premium | Monthly Premium |

Alaska | $698 | $116 |

Alabama | $648 | $108 |

Arkansas | $851 | $142 |

Arizona | $708 | $118 |

California | $911 | $152 |

Colorado | $849 | $142 |

Connecticut | $771 | $129 |

Washington DC | $713 | $119 |

Delaware | $808 | $135 |

Florida | $1,162 | $194 |

Georgia | $769 | $128 |

Hawaii | $540 | $90 |

Iowa | $575 | $96 |

Idaho | $628 | $105 |

Illinois | $642 | $107 |

Indiana | $594 | $99 |

Kansas | $800 | $133 |

Kentucky | $925 | $154 |

Louisiana | $1,152 | $192 |

Massachusetts | $651 | $109 |

Maryland | $718 | $120 |

Maine | $550 | $92 |

Michigan | $1,267 | $211 |

Minnesota | $699 | $117 |

Missouri | $844 | $141 |

Mississippi | $751 | $125 |

Montana | $775 | $129 |

North Carolina | $505 | $84 |

North Dakota | $661 | $110 |

Nebraska | $760 | $127 |

New Hampshire | $480 | $80 |

New Jersey | $751 | $125 |

New Mexico | $637 | $106 |

Nevada | $872 | $145 |

New York | $846 | $141 |

Ohio | $463 | $77 |

Oklahoma | $773 | $129 |

Oregon | $666 | $111 |

Pennsylvania | $669 | $112 |

Rhode Island | $937 | $156 |

South Carolina | $733 | $122 |

South Dakota | $720 | $120 |

Tennessee | $629 | $105 |

Texas | $749 | $125 |

Utah | $657 | $110 |

Virginia | $513 | $86 |

Vermont | $528 | $88 |

Washington | $604 | $101 |

Wisconsin | $540 | $90 |

West Virginia | $715 | $119 |

Wyoming | $730 | $122 |

The difference between the cheapest car insurance state (Ohio) and the most expensive (Michigan) is over $800 per six-month policy period. This means drivers in Michigan pay over $130 per month more for car insurance than do Ohioan drivers! Learn more about auto insurance rates by state.

#### State minimum vs. full coverage: state-by-state cost analysis

Each state regulates its insurance laws, governing what coverage types drivers must carry and in what amounts. Nearly every state requires certain minimums for liability coverage, while some states may require additional coverage types such as personal injury protection (PIP) or uninsured/underinsured coverage.

Below, you'll find a state-by-state rundown of the average six-month premiums for the minimum liability limit versus a "full coverage" policy. While "full coverage" is generally a combination of other coverage types, in this case, it refers to higher liability limits (50/100/50) and collision and comprehensive deductibles at $500 each — a fairly typical coverage level in the United States.

###### AVERAGE 6-MONTH INSURANCE PREMIUMS — FULL COVERAGE VS. STATE MINIMUM

State | State Minimum Liability | Full Coverage |

Alaska | $241 | $698 |

Alabama | $244 | $648 |

Arkansas | $295 | $851 |

Arizona | $334 | $708 |

California | $315 | $911 |

Colorado | $318 | $849 |

Connecticut | $360 | $771 |

Washington, D.C. | $319 | $713 |

Delaware | $436 | $808 |

Florida | $539 | $1,162 |

Georgia | $327 | $769 |

Hawaii | $211 | $540 |

Iowa | $150 | $575 |

Idaho | $199 | $628 |

Illinois | $238 | $642 |

Indiana | $221 | $594 |

Kansas | $248 | $800 |

Kentucky | $388 | $925 |

Louisiana | $483 | $1,152 |

Massachusetts | $266 | $651 |

Maryland | $333 | $718 |

Maine | $224 | $550 |

Michigan | $613 | $1,267 |

Minnesota | $299 | $699 |

Missouri | $298 | $844 |

Mississippi | $283 | $751 |

Montana | $230 | $775 |

North Carolina | $201 | $505 |

North Dakota | $190 | $661 |

Nebraska | $206 | $760 |

New Hampshire | $185 | $480 |

New Jersey | $371 | $751 |

New Mexico | $252 | $637 |

Nevada | $437 | $872 |

New York | $417 | $846 |

Ohio | $174 | $463 |

Oklahoma | $296 | $773 |

Oregon | $320 | $666 |

Pennsylvania | $226 | $669 |

Rhode Island | $451 | $937 |

South Carolina | $323 | $733 |

South Dakota | $158 | $720 |

Tennessee | $199 | $629 |

Texas | $286 | $749 |

Utah | $320 | $657 |

Virginia | $197 | $513 |

Vermont | $166 | $528 |

Washington | $295 | $604 |

Wisconsin | $181 | $540 |

West Virginia | $276 | $715 |

Wyoming | $167 | $730 |

#### Average car insurance rates by region

Car insurance costs vary by region, as well. For example, in the Midwest, Michigan is expensive, but the cheaper car insurance offered in Ohio ($463), Indiana ($594), Illinois ($642) and Wisconsin ($540), help lower the overall average.

###### AVERAGE INSURANCE PREMIUMS BY REGION

Region | Average 6-Month Premium |
---|---|

New England | $619 |

Great Lakes | $697 |

Great Plains | $726 |

Southwest | $737 |

Rocky Mountains | $748 |

Mideast | $753 |

Southeast | $777 |

Far West | $796 |

#### Compare auto insurance rates now!

### Car insurance quotes by vehicle

It goes without saying: your vehicle contributes to the cost of your car insurance. Every single vehicle will generate a unique premium based on its vehicle identification number (VIN). Insurance companies use the VIN to assess your vehicle’s mileage, accident history and other characteristics that are factored into your premium. It’s difficult to give an average cost of car insurance by vehicle — below are some national averages.

###### AVERAGE COST OF CAR INSURANCE BY VEHICLE TYPE

### How car insurance premiums are calculated

An “average rate” is hard to calculate, thanks to the myriad rating factors contributing to any driver's auto insurance premium. For instance, homeowners are likely to pay less for car insurance in general. Your driving record is also a major contributor, as those with a DUI are more likely to pay far higher rates for insurance as well.

Car insurance is designed — and priced — to suit each individual driver, accurately estimating the risk they represent to an insurer. While car insurance quote pricing varies by driver, it also varies by company. Between the cheapest company and the most expensive, you might find a substantial price gap. This is because every insurer weighs different factors when underwriting a policy.

It's important to take the national average cost of car insurance with a grain of salt. The best way to find an affordable policy, consult an insurance agent or compare car insurance online.

#### Compare rates and find a policy today!

### Average car insurance rate FAQs

#### What is the average cost of car insurance?

Across the U.S., the average annual premium is $1,483, or $124 per month. That's a decrease of 4% compared to 2020's national average of $1,548.

#### How much does car insurance cost in my state?

Your location — down to your specific ZIP code — is a critical rating factor when insurance companies calculate your premium. In addition, because auto insurance is regulated on the state level, each state's laws and regulations do make an impact on average rates. For instance, Michigan is consistently the most expensive state for car insurance largely due to mandated coverage requirements enforced by law.

Other expensive states include Louisiana, Florida, Kentucky, Rhode Island, Nevada and California. Some of the cheapest states for car insurance include Ohio, New Hampshire, North Carolina, Virginia and Vermont.

#### Which car insurance companies have the most affordable rates?

In our survey of top car insurance companies, Nationwide was the cheapest for the average driver profile. GEICO was a close second. Keep in mind that this individual profile likely won't match yours exactly. The best way to find a budget-friendly rate is to shop around for quotes before the end of every policy period.

#### How much is car insurance for a young driver in their 20s?

On average, drivers aged 20 to 29 pay $1,887 per year for auto insurance. That's $944 for a six-month policy or $157 per month. Young drivers in their 20s paid 27% more than the national average.

### Additional resources

If you want to learn more about car insurance, see our additional articles:

### About The Zebra

The Zebra is not an insurance company. We’re an independent, unbiased partner for consumers, on a mission to help you compare insurance options apples-to-apples, so you can make a truly informed decision. We’re proud because:

- We’re the first to compare all the major insurance companies side-by-side. The information provided on those insurers here is intended to help inform and educate consumers before they decide where to spend their hard-earned cash.
- We have no stake in which insurance company you choose — we simply want to offer you unbiased, fast, side-by-side comparisons of your insurance options.

This article was written by one of The Zebra’s insurance experts . Each article is thoroughly researched to ensure we provide readers the most accurate — and helpful — information possible. That’s insurance in black and white.®

## 6.9: Average Reservoir Pressure Estimating Techniques

Average reservoir pressures are used for characterizing a reservoir, computing its oil/gas in place, and predicting future behavior. In addition to these uses, the average reservoir pressure is required to find a quantitative use in volumetric-balance calculations of oil/gas in place in a reservoir. In this section we will present various methods to calculate average reservoir pressure in a gas reservoir.

### Horner MBH Method

The average reservoir pressure for a finite or bounded reservoir may be estimated as shown below using the values of *m* and ? />obtained from the Horner plot and the MBH curves.3 From Equation 6 21 for />,

where Eq. 6 22 is the defining equation ? />. The material balance equation may be written in terms of pseudopressure with substitution for dimensionless quantities as

Subtracting Eq. 6 22 from Eq. 6 24 gives

*m* is the absolute value of the slope of the straight-line section of the Horner plot:

*F* is the MBH dimensionless pressure at *t* _{DA}, and the *t* _{DA} is the dimensionless time:

*t* _{P} is a pseudoproduction time in hours and is calculated using Eq. 6 17 *?* ( *p**) is the value of *?* ( *p* _{ws}) corresponding to />, from the extrapolated semilog straight line. *F* may be obtained from Table B 1 or Figures B 1 through B 5 corresponding to the appropriate well reservoir configuration and reservoir shape. Values of *t* _{DA} may be calculated from Eq. 6 28.

## Marijuana Law Enforcement Cost States An Estimated $3.6 Billion In 2010: ACLU

States together spent somewhere around $3.6 billion enforcing marijuana possession laws in 2010, according to a new study by the American Civil Liberties Union, entitled “The War On Marijuana In Black and White.” That's the authors' "best estimate," though approximations using different methodologies put the cost as high as $6 billion and as low as $1.2 billion.

The paper grabbed headlines Tuesday with its finding that blacks are nearly four times as likely as whites to be arrested for possessing marijuana, despite both races using the drug at about the same rate.

Here are some most startling numbers from the ACLU’s report with regards to the cost of enforcing marijuana laws:

**$20 billion:** The amount states will spend enforcing marijuana laws over the next six years.

**$900:** The minimum per-capita cost spent by California, Nevada and Washington on criminal justice for marijuana offenders.

**$750:** The low-level estimate that states pay for each marijuana arrest.

**$95:** The national average per-diem cost of housing an inmate arrested due to a marijuana-related offense.

**$2:** The average amount communities spend each day on marijuana supervision.