## Frequency Exercise

1. The following set of data shows the number of cars owned by 40 households in a town:

4, 3, 1, 1, 2, 1, 6, 1, 3, 1, 4, 5, 1, 1, 1, 4, 1, 2, 1, 4, 2, 3, 5, 3, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 4, 3, 2, 1, 2, 1

a. Complete the frequency table below to summarise these numbers and find the mean number of cars owned.

b. Show this distribution on an appropriate graph.

 Number of cars (x) Tally frequency (f) f . x 1 2 3 4 5 6 Totals

2. The following frequency table shows the results of an examination (%) of 600 students.

 Exam mark Frequency (f) Midpoint(x) f . x 1 − 20 87 10.5 21 − 40 324 41 − 60 158 61 − 80 23 81 -100 8 Totals

a. Draw a bar graph to show this data.

b. Find the mean and modal interval.

3

The heights of a squad of 20 rugby players are shown below:

193, 174, 169, 198, 201, 178, 188, 179, 183, 188

194, 204, 203, 185, 195, 209, 193, 197, 196, 168

a. Complete the grouped frequency table below:

 Height (cm) Frequency (f) Midpoint (x) 160 − 170 170 − 180 180 − 190 190 − 200 200 − 210

(160 − 170 means greater or equal to 160 and less than 170)

b. Draw a histogram to show these heights.

c. Find the approximate mean of the heights.

d. What is the modal class or interval?

e. Complete the cumulative frequency table below and sketch a cumulative frequency graph.

 Height (cm) Cumulative Frequency(less than x) 150 0 160 170 180 190 200 210

f. Use the cumulative frequency graph to find:

(i) Median

(ii) Upper quartile

(iii) Lower quartile

(iv) 80th percentile

(v) 10th percentile       