MEAN, MEDIAN, MODE, AND RANGE

Mean Median

Mode Range

Concept: The words mean, median, mode, and range are used in the study of statistics. Perhaps an example will help to explain the meanings of these words.

Paul kept track of his blood sugar readings for one week. These were the readings. 105 95 110 85 90 100 90
If we arrange these readings from smallest to largest, they look like this. 85 90 90 95 100 105 110
The mean of a group of numbers is the average. To find the average of a group of numbers, add the integers together and divide the sum of the integers by the total number of integers. 1 2 3 4 5 6 7 85 + 90 + 90 + 95 + 100 + 105 + 110 = 675 675 ÷ 7 = 96.4 The mean in this group of numbers is 96.4.
The median of a group of numbers is the middle integer. 85 90 90 95 100 105 110
The median in this group of numbers is 95. When there are an even number of integers in a group, the median will be the average of the middle two integers.
The mode is the number which occurs more than any other number. 85 90 90 95 100 105 110 MODE The mode in this group of numbers is 90. There can be more than one mode in a group of numbers.
The range is the difference between the smallest number and the largest number. RANGE 85 90 90 95 100 105 110 110 – 85 = 25 The range is 25.

Steps for Solving Median Problems

Step 1 | Arrange the list of numbers in ascending order (smallest to largest).
Step 2 | Count the number of integers in the list.
Step 3 | If the number of integers in the list is odd, determine the middle integer. That is the median.
Step 4 | If the number of integers in the list is even, determine the middle two integers and average them. The average of those two numbers is the median.
Step 5 | Write the final answer.

Example The eel eating contestants ate for 30 minutes. Records show the 5 contestants ate the following values of eel: $169.00, $186.00, $173.00, $176,00, $151.00. What was the median value of eel eaten?

Step 1 | Arrange the list of numbers in ascending order (smallest to largest). |
| $151.00 $169.00 $173.00 $176.00 $186.00 |
Step 2 | Count the number of integers in the list. |
| 1 2 3 4 5 $151.00 $169.00 $173.00 $176.00 $186.00 | 5 integers = odd
Step 3 | If the number of integers in the list is odd, determine the middle integer. That is the median. |
| 1 2 3 4 5 $151.00 $169.00 $173.00 $176.00 $186.00 | $173.00 is the middle integer and the median.
Step 4 | If the number of integers in the list is even, determine the middle two integers and average them. The average of those two numbers is the median. | Does not apply in this problem.
Step 5 | Write the final answer. | $173.00