## Central Tendency Exercise

1. The weights of 5 kg bags of potatoes are given below in kilograms to 2 significant figures.

5.2 kg, 5.3 kg, 5.1 kg, 5.1 kg, 5.3 kg, 5.4 kg, 5.2 kg, 5.1 kg, 5.0 kg, 4.9 kg, 5.5 kg, 5.3 kg, 5.2 kg, 5.1 kg

Find the mean, median and mode of these weights.

2. Use a calculator in statistical mode to find the mean of:

a. 5, 7, 3, 5, 7, 8, 9, 10
b. 405, 285, 617, 435 , 849, 312, 908, 304, 172
c. 0.75, 0.95, 0.34, 0.68, 0.59, 1.04, 1.19, 0.59

3. Find the mean, median and mode of the following frequency distribution of the lengths of chips from a takeaway bar..

 x (cm) 4 5 6 7 8 9 10 frequency 4 7 12 20 6 4 1

4. The frequency table below shows the heights of 100 people:

 Heights (cm) Midpoint (x) Frequency (f) f.x 130 - 7 140 - 13 150 - 21 160 - 28 170 - 13 180 - 10 190 − 200 8 Totals

a. Find the modal interval.

b. Calculate the mean of the distribution.

c. In which interval would the median lie?

5. State whether the following would produce discrete or continuous data:

a. The hat sizes of a brass band
b. The capacity of containers
c. The number of spectators at soccer games
d. The number of pets in each of 100 households
e. The times of 800 metre runners

6. Explain why the mean of a grouped frequency distribution is only an approximation.

7. The mean of four numbers is 27. Another number brings the mean to 30. What is the value of the new number?

8. The mean of five numbers is 7 and the mean of five different numbers is 9. What is the mean of all ten numbers together?

9. The mean of these numbers is 18.

15, x, 12, 18, 20, 21, 22

What is the value of x?