# Statistics: 1001 Practice Problems For Dummies (+ Free Online Practice)

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Published: May 24, 2022

## Overview

Become more likely to succeed—gain stats mastery with Dummies

Statistics: 1001 Practice Problems For Dummies gives you 1,001 opportunities to practice solving problems from all the major topics covered in Statistics classes—in the book and online! Get extra help with tricky subjects, solidify what you’ve already learned, and get in-depth walk-throughs for every problem with this useful book. These practice problems and detailed answer explanations will help you gain a valuable working knowledge of statistics, no matter what your skill level. Thanks to Dummies, you have a resource to help you put key stats concepts into practice.

• Work through practice problems on all Statistics topics covered in school classes
• Access practice questions online to study anywhere, any time
• The material presented in Statistics: 1001 Practice Problems For Dummies is an excellent resource for students, as well as parents and tutors looking to help supplement Statistics instruction.

Statistics: 1001 Practice Problems For Dummies (9781119883593) was previously published as 1,001 Statistics Practice Problems For Dummies (9781118776049). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.

Statistics: 1001 Practice Problems For Dummies Cheat Sheet

There are many types of statistics problems, including the use of pie charts, bar graphs, means, standard deviation to correlation, regression, confidence intervals, and hypothesis tests. To be successful, you need to be able to make connections between statistical ideas and statistical formulas. Through practice, you see what type of technique is required for a problem and why, as well as how to set up the problem, work it out, and make proper conclusions. Most statistics problems you encounter likely involve terminology, symbols, and formulas. No worries! This Cheat Sheet gives you tips for success.

## Articles From The Book

74 results

Statistics Articles

### How to Use the T-table to Solve Statistics Problems

The t-table (for the t-distribution) is different from the z-table (for the z-distribution). Make sure you understand the values in the first and last rows. Finding probabilities for various t-distributions, using the t-table, is a valuable statistics skill.

## How to use the t-table to find right-tail probabilities and p-values for hypothesis tests involving t:

1. First, find the t-value for which you want the right-tail probability (call it t), and find the sample size (for example, n).
2. Next, find the row corresponding to the degrees of freedom (df) for your problem (for example, n – 1). Go across that row to find the two t-values between which your t falls. For example, if your t is 1.60 and your n is 7, you look in the row for df = 7 – 1 = 6. Across that row you find your t lies between t-values 1.44 and 1.94.
3. Then, go to the top of the columns containing the two t-values from Step 2. The right-tail (greater-than) probability for your t-value is somewhere between the two values at the top of these columns. For example, your t = 1.60 is between t-values 1.44 and 1.94 (df = 6); so the right tail probability for your t is between 0.10 (column heading for t = 1.44); and 0.05 (column heading for t = 1.94).

The row near the bottom with Z in the df column gives right-tail (greater-than) probabilities from the Z-distribution.

Use the t table to find t*-values (critical values) for a confidence interval involving t:
1. Determine the confidence level you need (as a percentage).
2. Determine the sample size (for example, n).
3. Look at the bottom row of the table where the percentages are shown. Find your % confidence level there.
4. Intersect this column with the row representing your degrees of freedom (df).
This is the t-value you need for your confidence interval. For example, a 95% confidence interval with df=6 has t*=2.45. (Find 95% on the last line and go up to row 6.)

## Practice solving problems using the t-table sample questions below

1. For a study involving one population and a sample size of 18 (assuming you have a t-distribution), what row of the t-table will you use to find the right-tail (“greater than”) probability affiliated with the study results?

The study involving one population and a sample size of 18 has n – 1 = 18 – 1 = 17 degrees of freedom.

2. For a study involving a paired design with a total of 44 observations, with the results assuming a t-distribution, what row of the table will you use to find the probability affiliated with the study results?

A matched-pairs design with 44 total observations has 22 pairs. The degrees of freedom is one less than the number of pairs: n – 1 = 22 – 1 = 21.

3. A t-value of 2.35, from a t-distribution with 14 degrees of freedom, has an upper-tail (“greater than”) probability between which two values on the t-table?

Using the t-table, locate the row with 14 degrees of freedom and look for 2.35. However, this exact value doesn’t lie in this row, so look for the values on either side of it: 2.14479 and 2.62449. The upper-tail probabilities appear in the column headings; the column heading for 2.14479 is 0.025, and the column heading for 2.62449 is 0.01.

Hence, the upper-tail probability for a t-value of 2.35 must lie between 0.025 and 0.01.

Statistics Articles

### How to Use the Z-Table

You can use the z-score table to find a full set of "less-than" probabilities for a wide range of z-values using the z-score formula. Below you will find both the positive z-score and negative z-score table. The problem examples below the table will help you learn how to use it.

## Z Score Table Sample Problems

Use these sample z-score math problems to help you learn the z-score formula.
1. What is P (Z ≤ 1.5) ?

To find the answer using the z-table, find where the row for 1.5 intersects with the column for 0.00; this value is 0.9332. The z-table shows only "less than" probabilities so it gives you exactly what you need for this question. Note: No probability is exactly at one single point, so:

P (Z ≤ 1.5) = P (Z < 1.5)
2. What is P (Z ≥ 1.5) ?

Use the z-table to find where the row for 1.5 intersects with the column for 0.00, which is 0.9332. Because the z-table gives you only "less than" probabilities, subtract P(Z < 1.5) from 1 (remember that the total probability for the normal distribution is 1.00, or 100%):

P (Z ≥ 1.5) = 1 – P (Z < 1.5) = 1 – 0.9332 = 0.0668
3. What is P (–0.5 ≤ Z ≤ 1.0) ?

To find the probability that Z is between two values, use the z-table to find the probabilities corresponding to each z-value, and then find the difference between the probabilities.

Here, you want the probability that Z is between –0.5 and 1.0. First, use the z-table to find the value where the row for –0.5 intersects with the column for 0.00, which is 0.3085. Then, find the value where the row for 1.0 intersects with the column for 0.00, which is 0.8413.

Because the z-table gives you only "less than" probabilities, find the difference between the probability less than 1.0 and the probability less than –0.5:

P (–0.5 ≤ Z ≤ 1.0) = P (Z ≤ 1.0) – P (Z ≤ –0.50) = 0.8413 – 0.3085 = 0.5328
4. What is P (–1.0 ≤ Z ≤ 1.0) ?

To find the probability that Z is between two values, use the z-table to find the probabilities corresponding to each z-value, and then find the difference between the probabilities.

Here, you want the probability that Z is between –1.0 and 1.0. First, use the z-table to find the value where the row for –1.0 intersects with 0.00, which is 0.1587. Then, find the value where the row for 1.0 intersects with the column for 0.00, which is 0.8413.

Because the z-table gives you only "less than" probabilities, find the difference between probability less than 1.0 and the probability less than –1.0:

P (–1.0 ≤ Z ≤ 1.0) = P (Z ≤ 1.0) – P (Z ≤ –1.0) = 0.8413 – 0.1587 = 0.6826

Statistics Articles

### Understanding the Statistical Mean and the Median

Descriptive statistics are statistics that describe data. Two of the staple ingredients of descriptive statistics are the mean and median. Your first job in analyzing data is to identify, understand, and calculate these descriptive statistics. Solve the following problems about means and medians.

## Sample questions

1. To the nearest tenth, what is the mean of the following data set? 14, 14, 15, 16, 28, 28, 32, 35, 37, 38

Use the formula for calculating the mean

where

and n is the number of values in the data set.

In this case, x = 14 + 14 + 15 + 16 + 28 + 28 + 32 + 35 + 37 + 38 = 257, and n = 10. So the mean is

2. To the nearest tenth, what is the mean of the following data set? 0.8, 1.8, 2.3, 4.5, 4.8, 16.1, 22.3

Use the formula for calculating the mean

where

and n is the number of values in the data set.

In this case, x = 0.8 + 1.8 + 2.3 + 4.5 + 4.8 + 16.1 + 22.3 = 52.6, and n = 7. So the mean is

The question asks for the nearest tenth, so you round to 7.5.

3. To the nearest tenth, what is the median of the following data set? 6, 12, 22, 18, 16, 4, 20, 5, 15

To find the median, put the numbers in order from smallest to largest:

4, 5, 6, 12, 15, 16, 18, 20, 22

Because this data set has an odd number of values (nine), the median is simply the middle number in the data set: 15.

4. To the nearest tenth, what is the median of the following data set? 14, 2, 21, 7, 30, 10, 1, 15, 6, 8

To find the median, put the numbers in order from smallest to largest:

1, 2, 6, 7, 8, 10, 14, 15, 21, 30

Because this data set has an even number of values (ten), the median is the average of the two middle numbers:

5. Compare the mean and median of a data set that has a distribution that is skewed right.

Answer: The mean will have a higher value than the median.

A data set distribution that is skewed right is asymmetrical and has a large number of values at the lower end and few numbers at the high end. In this case, the median, which is the middle number when you sort the data from smallest to largest, lies in the lower range of values (where most of the numbers are).

However, because the mean finds the average of all the values, both high and low, the few outlying data points on the high end cause the mean to increase, making it higher than the median.

6. Compare the mean and the median of a data set that has a symmetrical distribution.

Answer: The mean and median will be fairly close together.

When a data set has a symmetrical distribution, the mean and the median are close together because the middle value in the data set, when ordered smallest to largest, resembles the balancing point in the data, which occurs at the average.

If you need more practice on this and other topics from your statistics course, visit 1,001 Statistics Practice Problems For Dummies to purchase online access to 1,001 statistics practice problems! We can help you track your performance, see where you need to study, and create customized problem sets to master your stats skills.