18. Histograms

Question 1 

Below is a grouped frequency table for the times take for students to run a 100m race. Construct a histogram of the data.

Select the correct answer from the list below:

A:

B:

C:

D:

CORRECT ANSWER:   C

WORKED SOLUTION:

To create a histogram it is helpful to add two columns to the table, class width and frequency density. We find the frequency density by dividing the frequency by the class width.

To plot the histogram, we put the time on the x-axis and frequency density on the y-axis.

Level 6

Question 2

Below is a grouped frequency table for the heights of people surveyed on the street. Construct a histogram of the data. Round any values to 1 decimal place.

Select the correct answer from the list below:

A:

B:

C:

D:

CORRECT ANSWER:   A

WORKED SOLUTION:

To create a histogram, it is helpful to add two columns to the table, class width and frequency density. We find the frequency density by dividing the frequency by the class width.

To plot the histogram, we put the time on the x-axis and frequency density on the y-axis.

Level 6

Question 3

A group of people were asked their salaries, the data is shown in the histogram below. How many people were asked their salary?

Select the correct answer from the list below:

A: 89

B: 75

C: 40

D: 111

CORRECT ANSWER:  D: 111

WORKED SOLUTION:

To find out how many people each bar represents, we just need to multiply its height by its width.
2\times4=8
6\times2=12
2\times9=18
5\times4=20
5\times7=35
5\times2=10
5\times1.6=8

And now, all we need to do is add all of these together.

Level 6

Question 4

Below is a histogram of data for how high athletes could jump in high jump competition.

Given that 9 athletes jumped a height of at least 218cm, how many athletes competed in this event?

Select the correct answer from the list below:

A: 36

B: 27

C: 54

D: 75

CORRECT ANSWER:  B: 27

WORKED SOLUTION:

We need to find out how many people each individual square represents.
The question tells us that there were 9 athletes that jumped at least 218cm, which is represented below.

So, we know this total area represents 9 athletes. If we count all the little squares in red:

Because this area represents 9 athletes, we can divide it by 9 to find how much area one athlete represents.
9\text{ athletes }=225 \text{ squares}
1 \text{ athlete }=\frac{225}{9}=25 \text{ squares}

Now, if we find the rest of the area, we can find out how many more athletes took part. It is worth noting that each big square has 25 little squares in it, so each big square actually represents 1 athlete! There are 18 big boxes, meaning there are 18 more athletes. If we add this to our original 9, it will give us the total.

Level 6

Question 5

The histogram below represents the amount of time a 116 people spend watching TV each week. Find how many people spend 6 hours or less watching TV each week.

Select the correct answer from the list below:

A: 30

B: 54

C: 78

D: 40

CORRECT ANSWER:  A: 30

WORKED SOLUTION:

To start, we need to find the total area of (how many small squares are in) the histogram. We do this by multiply the height and width of each bar.

10\times4=40\text{ small squares}
5\times7=35\text{ small squares}
10\times12=120\text{ small squares}
15\times3=45\text{ small squares}
10\times5=50 \text{ small squares}

We can now find the total area by adding these together.

So, we can say that this area represents our total number of people surveyed.

To find how many squares represents one person, we need to divide by 116.

We now need to count how many small squares are in the first two bars (less than 6 hours), which we do by multiplying the same as above.

10\times4=40\text{ small squares}
5\times7=35\text{ small squares}

We then get their total area by adding them together.

Finally, we just need to divide this by the number of small squares that represents one person (2 small squares).

Level 6