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

Steps for Solving Intermediate 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 Dartanion bought spy costumes yearly for 9 years. He paid on average $65.89 per year. He remembered how much he paid for 8 of the years. They were: $80.00, $75.00, $53.00, $55.00, $86.00, $56.00, $69.00, $58.00. Can you tell him how much he paid for the other year?

Step A | In order to find the unknown price in this problem, we must first designate a variable representing the unknown price.
| N = unknown price
Step 1 | Add all the integers together.
Step B | We know from the question that the average (mean) of the nine integers, including the unknown price, is 65.89, so we set up the standard equation for finding the mean, substituting known values.
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 C | Solve the equation.
Step 3 | Write the final answer.
| He paid $61.00 for the other year.