Mean, Median, Mode, Range

Mean, Median, Mode, Range

We can analyze data in a number of ways to see how the numbers relate to one another. If you are looking at a set of test scores, think of what each value would show you about that set:

 MEAN The sum of the set of data divide by the number of addends, also called average. MEDIAN Middle number when the data are arranged in order MODE The number in a set of data that appears most often RANGE Describes how spread apart data is by taking the difference of the greatest value and least value

EXAMPLE

Shawndelle checked the prices of her 10 favorite books at Books by the Billion. The prices are listed below. Find the mean, median, mode, and range of the prices.

\$5   \$7   \$4   \$9   \$7   \$8   \$5   \$7   \$6   \$7

Strategy for Mean

The mean is the average.  Add the numbers and divide by how many numbers there are.

Solution

(5 + 7 + 4 + 9 + 7 + 8 + 5 + 7 + 6 + 7) ÷ 10

= 6.5

The mean is 6.5, or \$6.50.

Strategy for Median

Set the data in order from lowest to highest and find the middle number.

Solution

4  5  5  6  7  7  7  7  8  9

There are two middle numbers, 7 and 7. To find the median, you have to find the mean of those two numbers.

(7 + 7) ÷ 2 = 14 ÷ 2 = 7

The median is \$7.

Strategy for Mode

List the data in order and find the most frequently occurring number.

Solution

4  5  5  6  7  7  7  7  8  9

The mode is \$7.

Strategy for Range

Subtract the lowest number from the highest number.

Solution

4  5  5  6  7  7  7  7  8  9

9 − 4 = 5

The range is \$5.

Practice

1.  For a price comparison of three supermarkets, identical items were purchased in each store.  The results are listed below.

 Amount spent Store 1 \$40.74 Store 2 \$39.45 Store 3 \$38.57
a)  What is the range of the amounts spent?

b)  What is the average cost of items purchased at the three stores?

2.  Juan received test scores of 89, 90, 68, 82, 94, 96, and 79.

a)  What is his mean score?

b)  What is his median score?

3.  A local newspaper reports the mean price of a house sold in the village each week.  Houses sold for \$90,000, \$86,100, \$79,800, and \$93,000.  Find the mean price.

4.  A library's records show the number of books borrowed on each day last week.  Find the median of books borrowed.

 Mon Tue Wed Thur Fri Sat 450 385 410 596 482 491