Math Background

Mean, Median, and Mode: Overview

In Grade 4, your students will learn various ways to collect and organize data. They learned to collect data using a tally chart in Grade 3. Typically, a tally chart is used when several things are being counted at once, such as in a survey. The tally chart below shows the results of a survey in which students identified the type of apple they like to have for a snack.

tally chart

Line plots are another way to organize data as it is being collected. The line plot below shows the amount of money 8 students spent on snacks.

line plot

When students are familiar with reading line plots, introduce them to the different ways to describe data.

Range is the difference between the greatest and least number in a data set.

The range for the amount of money students spent on snacks is $5 − $1, or $4.

Mode is the number that occurs most often in a data set. Some data sets have don't have a mode; others have more than one mode.

The mode for the amount of money students spent is $4.

Mean is sometimes called the average. To find the mean, add the numbers and divide the sum by the number of addends.

$1 + $1 + $2 + $3 + $4 + $4 + $4 + $5 = $24

$24 ÷ 8 = $3

The mean for the amount of money students spent is $3.

The median is the middle number in a data set that is ordered from least to greatest. When there are two middle numbers, the median is the mean of these two numbers.

$1 $1 $2 $3 $4 $4 $4 $5

$3 + $4 = $7

$7 ÷ 2 = $3.50

The median for the amount of money students spent is $3.50.

An outlier is a number that is distant from most of the other data. The data shown on this line plot does not have an outlier. If one student had spent $8 on snacks, $8 would be an outlier. Some data sets have one outlier; others have more than one outlier.

Encourage your students to use range, mean, median, mode, and outlier when they describe data sets.

When you want to compare data, display it on a bar graph. A double bar graph can be used to compare two sets of data, usually about the same topic. The double bar graph below shows the favorite sports of third and fourth graders.

double bar graph

Line graphs are used to show how data changes over time. The line graph below shows the change in temperature from 5:00 A.M to 8:00 P.M.

line graph

Show your students graphs that cover a variety of topics; for example, graphs from science and social studies books. Have students bring graphs in from home that they find in newspapers and magazines. This activity will help them to appreciate the relevance of graphs in our world.

Probability is a way of describing the likelihood that an event will occur. The transparent bag below contains 7 marbles. Five of the marbles are red. Two of the marbles are blue.

transparent bag of 7 marbles

An outcome is a result in a probability experiment. If you pick a marble out of the bag without looking, you can pick a red marble or you can pick a blue marble.

The probability of picking a red marble is 5 out of 7, or five sevenths. It is likely that you will pick a red marble.

The probability of picking a blue marble is 2 out of 7, or two-sevenths. It is unlikely that you will pick a blue marble.

The probability of picking a yellow marble is 0 out of 7, or zero-sevenths. It is impossible that you will pick a yellow marble.

The probability of picking a red marble or a blue marble is 7 out of 7, or seven-sevenths. It is certain that you will pick a red marble or a blue marble.

Suppose that 15 campers in a group of 19 are wearing long pants. The other 4 campers are wearing shorts. If the camp counselor picks one student to go for water, what is the probability that the camper will be wearing shorts? (four-nineteenths) Is it likely, unlikely, impossible, or certain that the camper will be wearing shorts? (unlikely)


Houghton Mifflin Math Grade 4