The histogram gives information about the age of the members of a local club. The club has in total 29 members whose age is between 30 and 40. Part a) Work out the number of members who are younger than 18 years old. Part b) Can you precisely find out from this histogram how many members are older than 90 years old? You must justify your answer.
The frequency density on a histogram can be calculated by dividing the frequency by the class width. We’re told in the question that the club has 29 members whose ages between 30 and 40. This means that the area of this bar is equal to 29. The width of the bar is equal to 10 as 40 minus 30 equals 10.
We can, therefore, calculate the frequency density of members between 30 and 40 years of age by dividing 29 by 10. The frequency density is equal to 29 divided by 10. This is equal to 2.9. This means that the height of the bar is equal to 2.9.
There are 29 squares between this point and the bottom of the 𝑦-axis. Dividing 29 by 2.9 gives us 0.1. This means that each little square on the 𝑦-axis is equal to 0.1. We can, therefore, label the frequency density axis as shown on the graph: zero, one, two, three, and four.
The question asked us to calculate the number of members that are younger than 18 years old. This is the first bar on the histogram. The width of this bar is equal to 18 and the height is equal to 1.5.
The frequency or number of members is calculated by multiplying the frequency density by the width — in this case, 1.5 multiplied by 18. This is equal to 27 as one multiplied by 18 is 18 and 0.5 multiplied by 18 is equal to nine. Adding 18 and nine gives us 27. We can, therefore, say that there were 27 members of the club who are younger than 18 years old.
The second part of the question said the following. b) Can you precisely find out from this histogram how many members are older than 90 years old? You must justify your answer.
Using the method that we used in part a, we can work out that there were 10 members between 80 and 100. The final bar in the histogram has a width of 20 and a height of 0.5. 0.5 multiplied by 20 is equal to 10.
Despite being able to work out this information, our answer is no. We can work out how many members are between 80 and 100. But we don’t know how they’re distributed within that group. We don’t know whether some, all, or none of those 10 members are older than 90 years old. We only know that they were all aged between 80 and 100. This is because group data doesn’t tell you anything about the individuals, only that they are within that group.