To review these concepts, go to Statistics Word Problems Study Guide.

**Statistics Word Problems Practice Questions**

**Practice**

**Problems**

- Jake earned a 95, 92, 88, and 89 on his latest science exams. What is his mean score for these 4 tests?
- Using the information in question 1, Jake would like to have a 92 mean average in science class. If there will be a total of 5 exams, what score does he need on the next test to have a mean of 92 over the 5 exams?
- The average daily temperatures in degrees over one week were 40, 44, 50, 38, 58, 42, and 39, respectively. What is the median temperature for the week?
- The weights in pounds of 4 dogs at a kennel are 43, 65, 70, and 23. What is the median weight of these dogs?
- The times in seconds for 6 swimmers in a certain swimming event are 50, 58, 59, 42, 43, and 58, respectively. What is the mode?
- In a golf tournament, the scores of 5 different players were 74, 75, 75, 80, and 74. What is the mode of the set of golf scores?
- The prices of 4 different shirts at a store are $10.99, $9.99, $14.99, and $19.99. What is the range in prices of these shirts?

**Solutions**

*Read and understand the question*. This question is looking for the mean of a set of 4 numbers.*Read and understand the question*. This question is looking for the grade on the fifth exam when the grades of the first 4 exams and the mean of the 5 exams are given.*Read and understand the question*. This question is looking for the median value of a set of data.*Read and understand the question*. This question is looking for the median value of a set of data.*Read and understand the question*. This question is looking for the mode of a set of data.*Read and understand the question*. This question is looking for the mode of a set of data.*Read and understand the question*. This question is looking for the range of the prices of different shirts.

*Make a plan*. Find the sum of the set of numbers and then divide by the number of values in the set. There are 4 numbers in the set, so divide the sum by 4.

*Carry out the plan*. The sum of the numbers is 95 + 92 + 88 + 89 = 364. Divide the sum 364 by 4 to get 91. The mean of the numbers is 91.

*Check your answer*. To check this solution, work backward and multiply the average by 4 to check to see if the total is 364: 91 × 4 = 364. This solution is checking.

*Make a plan*. Find the total number of points needed on 5 tests to have an average of 92 by multiplying 92 by 5. Then, find the sum of the first 4 exams. Find the difference between these two amounts to find the score needed on the fifth exam.

*Carry out the plan*. The total needed on the 5 exams is 92 × 5 = 460. The sum of the exams taken so far is 95 + 92 + 88 + 89 = 364. The difference in these two amounts is 460 – 364 = 96. He needs a 96 on the fifth exam to have a mean average of 92.

*Check your answer*. To check this solution, find the average of the 5 exams to make sure it is equal to 92. The sum of the 5 exams is 95 + 92 + 88 + 89 + 96 = 460; 460 divided by 5 is equal to 92. This solution is checking.

*Make a plan*. The median of a set of data is the middle value in the list when the numbers are placed in order. Arrange the data values in order and find the middle value to find the median.

*Carry out the plan*. The numbers placed in order are 38, 39, 40, 42, 44, 50, 58. The middle value in this list is the fourth number, 42.

*Check your answer*. To check this solution, be sure that the numbers are placed in order and that no two values share the middle. There are 7 values, so the fourth value is the median. This solution of 42 is checking.

*Make a plan*. Arrange the data values in order, and find the middle value to find the median. If 2 values share the middle, find the mean of these 2 values to find the median.

*Carry out the plan*. The numbers in order are 23, 43, 65, 70. The values 43 and 65 share the middle. The mean of 43 and 65 is equal to = 54 The median is 54.

*Check your answer*. To check the solution, make sure that the values are in order. Since two values share the middle, the mean of these values is the median. The mean of 43 and 65 is 54, so this solution is checking.

*Make a plan*. The mode is the value that appears the most often in a set of data. Count the number of times each value appears to find the number that appears the most.

*Carry out the plan*. The list is 50, 58, 59, 42, 43, and 58. The number 58 appears in the list two times; each of the other values appears only once. The number 58 is the mode of this set of data.

*Check your answer*. To check this solution, double-check to be sure that no other value appears two or more times in the list. The number 58 is the only value that is repeated, so this solution is checking.

*Make a plan*. The mode is the value that appears the most often in a set of data. Count the number of times each value appears to find the number that appears the most.

*Carry out the plan*. The list is 74, 75, 75, 80, and 74. The numbers 74 and 75 each appear in the list two times; the other value appears only once. Therefore, the set has two modes and is called bimodal. The values 74 and 75 are the modes of this set of data.

*Check your answer*. To check this solution, double-check to be sure that no other values appear two or more times in the list. The numbers 74 and 75 each appear twice, so this answer is checking.

*Make a plan*. Find the difference between the most expensive shirt and the least expensive shirt to find the range.

*Carry out the plan*. The prices of the shirts are $10.99, $9.99, $14.99, and $19.99. The most expensive shirt is $19.99 and the least expensive shirt is $9.99. The difference is $19.99 – $9.99 = $10.00. The range is $10.

*Check your answer*. To check this solution, find the range again and be sure to subtract the greatest number from the least number in the set. The range for this set of values is $19.99 – $9.99 = $10.00, so this answer is checking.

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