Measures of Center and Spread: Data Word Problems

In this lesson, we will focus on solving data word problems that involve measures of center (mean, median) and spread (range, interquartile range). Understanding these concepts is crucial for interpreting data effectively on the SAT.

Example Problem

A classroom has the following test scores: 75, 85, 90, 70, and 80. Calculate the mean, median, and range of these scores.

Step 1: Calculate the Mean

To find the mean, sum all the scores and divide by the number of scores.

Sum of scores:
$75 + 85 + 90 + 70 + 80 = 400$
Number of scores:
$5$
Mean:
$\frac{400}{5} = 80$

Step 2: Calculate the Median

To find the median, first arrange the scores in ascending order: 70, 75, 80, 85, 90. Since there are 5 scores (an odd number), the median is the middle score.

Median:
$80$

Step 3: Calculate the Range

The range is the difference between the highest and lowest scores.

Highest score: 90
Lowest score: 70
Range:
$90 - 70 = 20$

Summary

• Mean: 80
• Median: 80
• Range: 20

Key Questions

• What is the mean of the following set of numbers: 60, 70, 80, 90, 100?
• How do you find the median in a set with an even number of values?
• What is the formula for calculating the range?
• If the highest score increases, how does it affect the range?
• Why is the median sometimes preferred over the mean?

Keywords

• Mean
• Median
• Range
• Data
• Spread