Albert Teen
powered by
Albert logo

YOU ARE LEARNING:

pointer
Mean from a Grouped Frequency Table
lessonMenuButton

Mean from a Grouped Frequency Table

lesson introduction

Mean from a Grouped Frequency Table

In grouped frequency tables, it is a little harder to find the mean as we only have groups of values. However, we can use group midpoints to find an estimation of the mean.

When data is grouped in a table, it is harder for us to calculate an accurate value for the mean as we do not have individual data. Therefore, we can only calculate an estimate.

1

The table shows the heights of a small group of students

We know there are 4 people with a height in the interval 150<h155150 < h\leq 155 , but we do not know exactly how tall each of these 4 people are.

block image
2

This is the formula for the mean

Without information on the individual height of the students, we will not be able to calculate a “sum” of all the heights. Instead we must use an estimate. A good estimate here is the midpoint of each interval.

block image
3

What is the midpoint of the group 150<h155150 < h \leq 155 ?

hint button
block image
4

The midpoint of 150<h155150 < h \leq 155 is 152.5152.5

In finding the midpoint, we assume 4 people with the height of 152.5cm, 3 people with the height of 157.5cm, 4 people with the height of 162.5cm and 3 people with the height of 167.5cm.

block image
5

Multiply the frequency and midpoints together

This will enable us to find an estimate for the sum of all heights.

block image
6

What is the value marked "?" in the table?

hint button
block image
7

The missing value is 650650

We can sum each of these values up to a total of 22352235

block image
8

Now we can find the mean

The sum of all values is 22352235, and the total number of values is 1414.

block image
9

What is the mean height? Give your answer to 1 decimal place

hint button
block image
10

The mean height is 159.6cm159.6cm

We can find this by dividing 223514=159.6\dfrac{2235}{14}=159.6. Remember that this is only an estimate for the mean, since we do not have any individual values.

block image