Histograms

The histogram represents the ages of the 500 members of a gym. The first bar represents the members aged at least 16 and under 20

Each member pays an annual fee based on their age.

Use the histogram to estimate the total annual fees paid by these members.

The table shows information about the salary of 90 employees.

Salary, s (£)	Frequency
0 s 20 000	44
20 000 s 40 000	22
40 000 s 60 000	14
60 000 s 80 000	5
80 000 s 100000	2
100 000 s 120 000	3

Complete the cumulative frequency table.

Salary, s (£)	Cumulative Frequency
s 20000	44
s 40000	66
s 60000
s 80000
s 100000
s 120000

Draw a cumulative frequency diagram to represent the data.

Estimate the number of employees with a salary less than £32 000

Two types of battery, P and Q, were tested. 100 of each type were put into clocks. The number of days each battery lasted was recorded.

The frequency table represents the results for type P.

On the grid, draw a cumulative frequency diagram to represent the data.

For type Q, the median was 126 days the interquartile range was 57 days.

Compare the number of days that types P and Q lasted. Make one statement about the average and one statement about the spread.

Use statistical measures to support your statements.

The table shows information about the height of 40 plants.

Draw a histogram to represent the heights.

190 people were asked how much they spent on takeaways one month. The table shows information about the results.

Amount, x (£)	Cumulative frequency
0 x 10	16
0 x 20	64
0 x 30	140
0 x 40	184
0 x 50	190

How many people spent more than £20 ?

Farah draws this cumulative frequency curve to represent the results.

Give two criticisms of her graph.

100 people were asked about the distance they travel from home to work. The table shows information about the results.

Distance, d (miles)	Frequency
0 d 5	21
5 d 10	24
10 d 20	37
20 d 40	18

Write down the greatest possible number of people who work from home.

One person is chosen at random.

Work out the probability that the person travels at least 10 miles.

The table is repeated.

Distance, d (miles)	Frequency
0 d 5	21
5 d 10	24
10 d 20	37
20 d 40	18

Draw a histogram to represent the results.

180 runners started a marathon. Some of the runners did not complete it.

The histogram represents the times of the runners who did complete the marathon.

How many runners did not complete the marathon?

The table shows information about the runners who did not complete the marathon.

Draw a box plot to represent the information.

The table shows information about the heights of 60 athletes.

Height, h (cm)	Frequency
150 h 160	4
160 h 170	12
170 h 180	35
180 h 190	7
190 h 200	2

Complete the cumulative frequency table.

Height, h (cm)	Cumulative frequency
h 150	0
h 160	4
h 170	16
h 180
h 190
h 200

Circle the class interval that contains the lower quartile.

Draw a cumulative frequency diagram to represent the data.

Estimate the number of the athletes whose height is more than 176 cm

61 students recorded how many hours they spent revising for a test. The histogram represents the results.

Work out an estimate of the mean time the 61 students spent revising. You may use the table to help you.

Give a reason why the answer to part (a) is an estimate.

75 people attend a clinic. Their ages are recorded and a cumulative frequency diagram is drawn.

A nurse makes a statement about the ages of the people at the clinic. He says, “More than twice as many people are in their 60s as in their 50s.” Is he correct?

Show working to support your answer.

A company makes tubes of toothpaste. The masses of 80 tubes are checked. A histogram is drawn to represent the data.

The company makes 28 000 tubes each day. Estimate how many tubes each day have a mass less than 122 grams.

The cumulative frequency graph represents the masses of 40 necklaces.

A jeweller buys every necklace with mass greater than 21 grams. Use the graph to estimate how many she buys.

The lowest mass was 3 grams. The highest mass was 28 grams. Draw a box plot to represent the data.

Here is some information about the ages of babies at a clinic.

Draw a histogram to represent the information.

A histogram is drawn to represent the heights of a sample of women. Three of the four bars are shown. The bar for 170 cm ≤ height 180 cm is missing.

There are 74 women in the sample. Complete the histogram.

The cumulative frequency graph shows information about the masses of 200 apples.

Estimate the median mass.

Apples with mass 90 grams or less cost 32p each. Apples with mass more than 90 grams cost 39p each. Estimate the total cost of the 200 apples.

Here is some information about the test marks of 120 students.

Mark, m	0 m 10	10 m 20	20 m 30	30 m 40	40 m 50
Frequency	20	28	40	20	12

Complete the cumulative frequency table.

Mark, m	m 10	m 20	m 30	m 40	m 50
Cumulative frequency	20	48

Draw a cumulative frequency graph.

Students who scored 15 marks or fewer take another test. Use your graph to estimate how many students take another test.

A sample of 50 eggs is taken from Farm A. The table shows information about the masses of the eggs from Farm A.

A sample of 50 eggs is taken from Farm B. The histogram shows information about the masses of the eggs from Farm B.

For medium eggs, 53 g mass 63 g The Farm A sample has more medium eggs than the Farm B sample. Using the table and the histogram, estimate how many more. You must show your working.

The cumulative frequency graph shows information about the masses of 50 apples.

Use the graph to estimate the median mass of the apples.

Estimate the proportion of the apples that have a mass greater than 115 grams.

Here is some information about the ages of people at a concert.

Age, x (years)	Frequency
10 x 15	8
15 x 25	24
25 x 40	30
40 x 70	39

Draw a histogram to represent the information.

Type A batteries and type B batteries were tested. The cumulative frequency diagram shows information about the battery life of type A.

Estimate the interquartile range for type A.

Estimate the number of type A batteries that had a battery life of more than 1600 hours.

The box plot shows information about the battery life of type B.

On average, which type had the greater battery life? Tick a box.

Using data from both diagrams, state how you chose your answer.

The histogram shows information about the speed of cars as they pass a checkpoint. The scale on the frequency density axis is missing.

The histogram shows information about 480 cars.

How many cars does the first bar represent?

Cars with a speed greater than 40 mph are over the speed limit. Use the histogram to estimate the number of cars that are over the speed limit.

Here is some information about the miles per gallon of 60 cars.

Draw a cumulative frequency graph.

Use the graph to work out the interquartile range.

miles per gallon

Here is some information about a tennis club.

There are 30 members with A < 20 There are 12 members with 65 A < 80 There are no members with A 80

Complete the histogram.

Work out the total number of members of the club.

Here is some information about the marks of 60 students in a test.

On the grid, draw a cumulative frequency graph.

Use your graph to estimate the lowest mark of the top 20% of students.

48 students completed some homework. This histogram shows information about the times taken.

Work out an estimate of the interquartile range. You must show your working.