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.

SPECIAL NOTE Solving Intermediate Range Problems often involves the use of multiple operations as well as the use of some basic algebraic equations. The Steps for Solving Intermediate Range Problems must be applied fluidly.

Steps for Solving Intermediate Range Problems

Step 1 | Arrange the list of numbers in ascending order (smallest to largest), or determine the beginning and end points of the numbers being dealt with.
Step 2 | Determine the difference between the smallest and largest numbers in the group. That is the range.
Step 3 | Write the final answer.

Example A dogmatic Don doused doorknobs for 3 days in the ditch. The mean value of the doorknobs is $180.67. The dogmatic Don could only remember 2 days worth of doorknob values due to a cleaning accident. They were $174.00 and $198.00. What is the range of doorknob values the dogmatic Don doused?

Step A | In order to find the range in this problem, we must first determine what the value of the third doorknob is. | N = value of third doorknob
Step B | To do this, we will use a basic algebraic equation which includes the two known doorknob values, a variable representing the value of the third doorknob, and the mean value of all three doorknobs. |
Step C | Solve the algebraic equation. |
| Now we can use the Steps For Solving Range Problems. |
Step 1 | Arrange the list of numbers in ascending order (smallest to largest). | 170, 174, 198 |
Step 2 | Determine the difference between the smallest and largest numbers in the group by subtracting the smallest from the largest. The difference is the range. | 198 - 170 28 |
Step 3 | Write the final answer. | 28 |