Data Handling

Question 1

Anna had been practising 100m freestyle swimming. At one point, her average time was 112 seconds. Her next lap took 108 seconds and that increased her average to 109 seconds. After her final lap increased her average to 105 seconds. How long did she take on her final lap?

Answer 1

Anna took 95 seconds on her final lap.

Question 2

The following are the temperatures recorded in a city over 7 days (in °C):
18, 21, 19, 22, 24, 20, 19
(a) Find the mean temperature.
(b) Find the median temperature.
(c) Find the range of the temperatures.

Answer 2

(a) ~ 17.6°C
(b) 21
(c) 6

Question 3

A shop records the number of customers visiting each day over two weeks:
120, 135, 140, 125, 130, 128, 136, 142, 125, 130, 140, 138, 132, 134
(a) Calculate the mean number of customers.
(b) Find the median number of customers.
(c) Determine the mode of the data.
(d) Find the range of the data.
(e) If the highest value was incorrectly recorded as 142 instead of 152, how would this affect the mean and range?

Answer 3

(a) Mean number of customers: 132.5
(b) Median number of customers: 133.0
(c) Mode of the data: 140, 125, 130 (each appears twice)
(d) Range of the data: 22 (142 - 120)

(e) If the highest value was incorrectly recorded as 142 instead of 152, the new mean would be 133.21 (rounded to two decimal places), and the new range would increase to 32 (152 - 120).