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 Basic Mean Problems

Step 1 | Add all the integers together.
Step 2 | Divide the sum of the integers by the total number of integers. (The quotient is generally, though not always, your final answer.)
Step 3 | Write the final answer.

Example The miles between cities were measured 8 times. The measurements were: 177, 197, 187, 178, 192, 152, 185, 173. What is the average measurement (rounded to the nearest hundredth)?

Step 1 | Add all the integers together. |
| 177 + 197 + 187 + 178 + 192 + 152 + 185 + 173 = 1441 | 1441
Step 2 | Divide the sum of the integers by the total number of integers. (The quotient is generally, though not always, your final answer.) |
| There are 8 integers in the equation. The sum of all the integers is 1441. Divide 1441 by 8. |
Step 3 | Write the final answer. | The average measurement is 180.13.