Question

The histogram below shows information about the

temperature at noon in some different cities on one
day.
a) Complete the grouped frequency table by
working out the values that should replace x, y and
2.
b) Calculate an estimate for the mean temperature.
If your answer is a decimal, give it to 1 d.p.
Frequency density
5-
3
N
1-
2
-∞
6
8
Temperature (°C)
10
12
Temperature, t (°C) Frequency
2≤t<4
4≤t<6
6≤ t < 10
x
Y
N

Answer 1

a. The values that should replace x, y and z are x = 3, y = 5, and z = 1.

b. An estimate for the mean temperature is 4.3.

In a frequency distribution table, all classes must have the same class width. In this context, we would develop a grouped frequency table for the data set by using a class width of 2 as follows;

Temperature, t (°C) Frequency

2 ≤ t ≤ 4 3

4 ≤ t ≤ 6 5

6 ≤ t ≤ 10 1

Therefore, the values that should replace x, y and z are;

x = 3

y = 5

z = 1

Part b.

In order to determine an estimate for the mean temperature, we would first find the midpoint of the data set;

Temperature, t (°C) Frequency Midpoint Frequency × Midpoint

2 ≤ t ≤ 4 3 (2+4)/2 = 2 3 × 2 = 6

4 ≤ t ≤ 6 5 (4+6)/2 = 5 5 × 5 = 25

6 ≤ t ≤ 10 1 (6+10)/2 = 8 1 × 8 = 8

Estimated mean = (6 + 25 + 8)/(3 + 5 + 1)

Estimated mean = 39/9

Estimated mean = 4.3333 ≈ 4.3.