Introduction to Statistics Word Problems
Statistics means never having to say you're certain.
—AUTHOR UNKNOWN
This lesson covers the measures of central tendencies such as mean, median, and mode. Word problems on these topics, as well as on range will also be explained.
There are three common measures of central tendencies. Each of these measures gives different types of information about the data in a set. The first type of measure is the mean.
Mean
The mean is commonly known as the average of the numbers in a data set. To find the mean, find the sum of the set of numbers and then divide by the total number of values in the set. Take the following example.
The heights of players on a basketball team in inches are 69, 73, 75, 66, and 72. What is the mean height of the players on this team?
Read and understand the question. This question is looking for the mean of a set of 5 numbers.
Make a plan. Find the sum of the set of numbers and then divide by the number of values in the set. There are 5 values in the set, so divide the sum by 5.
Carry out the plan. The sum of the numbers is 69 + 73 + 75 + 66 + 72 = 355. Divide the sum 355 by 5 to get 71. The average of the numbers is 71.
Check your answer. To check this solution, work backward and multiply the average by 5 to check to see if the total is 355: 71 × 5 = 355. This solution is checking.
What about the situation where the mean is given, but one or more of the data values are unknown? Use the strategy of working backward to find a missing value when the mean is known.
Charlie earned a 79, an 85, and an 88 on his first 3 history exams. What does he need to earn on his fourth test to have exactly an average of 85 for the 4 exams?
Read and understand the question. This question is looking for the grade on the fourth exam when the grades of the first 3 exams and the average of the 4 exams are given.
Make a plan. Find the total number of points needed on 4 tests to have an average of 85 by multiplying 85 by 4. Then, find the sum of the first 3 exams. Find the difference between these 2 amounts to find the score needed on the fourth exam.
Carry out the plan. The total needed on the four exams is 85 × 4 = 340. The sum total of the exams taken so far is 79 + 85 + 88 = 252. The difference in these 2 amounts is 340 – 252 = 88. He needs an 88 on the fourth exam.
Check your answer. To check this solution, find the average of the 4 exams to make sure it is equal to 85. The sum total of the 4 exams is 79 + 85 + 88 + 88 = 340 and 340 divided by 4 is equal to 85. This solution is checking.
Median
The median of a data set is the number in the middle of the set when the values are placed in order. If there is an even number of values in the set, find the average of the two numbers in the middle of the set. Read through the following example.
The heights of players on a basketball team in inches are 69, 73, 75, 66, and 72. What is the median height?
Read and understand the question. This question is looking for the median value of a set of data.
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 66, 69, 72, 73, 75. The middle value in this list is the third number, 72.
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 five values, so the third value is the median. This solution of 72 is checking.
A new player with a height of 70 inches joins the team. What is the new median height of the team?
Read and understand the question. This question is looking for the median value of a set of data.
Make a plan. Rearrange the data values in order and find the middle value to find the median. If two values share the middle, find the mean of these two values to find the median.
Carry out the plan. The numbers in order are 66, 69, 70, 72, 73, 75. The values 70 and 72 share the middle. The mean of 70 and 72 is equal to = 71. The median is 71.
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 70 and 72 is 71, so this solution is checking.
Mode
The mode of a set of data is the value that appears the most in the set.
The number of points scored by a basketball team in five games is 68, 72, 74, 66, and 72. What is the mode of the points scored?
Read and understand the question. This question is looking for the mode of a set of data.
Make a plan. The mode is the value that appears most often in a set of data. Count the number of times each value appears to find the number that appears most.
Carry out the plan. The number 72 appears in the list two times; each of the other values appears only once. The number 72 is the mode of this set of data.
Check your answer. To check this solution, doublecheck to be sure that no other value appears two or more times in the list. The number 72 is the only value that is repeated, so this solution is checking.
Tip:
If two modes appear in a data set, the set is considered to be bimodal. If no value appears more than any other in the set, the set is considered to have no mode.

While mean, median, and mode are measures of central tendency, range is a measure of dispersion, or variability.
Range
The range of a set of data is the difference between the greatest value and the least value in the set.
The heights of players on a basketball team in inches are 68, 72, 74, 66, and 72. What is the range of the heights of the players?
Read and understand the question. This question is looking for the range of heights of five basketball players.
Make a plan. Find the difference between the tallest player and the shortest player to find the range.
Carry out the plan. The tallest player is 74 inches and the shortest is 66 inches. The difference is 74 – 66 = 8. The range is 8 inches.
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 74 – 66 = 8, so this solution is checking.
Tip:
These four statistics can be summarized as the following:
The mean is the average value.
The median is the middle value after the data has been ordered.
The mode is the value the occurs the most often.
The range is the difference between the highest and lowest values.

Find practice problems and solutions for these concepts at Statistics Word Problems Practice Questions.