Histograms Worksheet (Page 2 of 2) in pdf

Histograms Worksheet Page 2

15) (a) From the table, the frequency density for the first class is 20 ÷ 10 = 2

So the height of this bar on the histogram is 2, which enables you to scale the vertical axis.

The frequencies (areas) of the other bars given are:

10-15: 3 × 5 = 15 students

15-30: 4 × 15 = 60 students

(b) The frequency desities of the missing bars are:

30-50: 62 ÷ 20 = 3.1

50-60: 23 ÷ 10 = 2.3

f. d.

11) (a) Comparing first bar of histogram with first entry in table, height of first bar = freq density = 15÷10 = 1.5

So each small mark on vertical axis is 0.1.

Second bar (150-160) = 10 × 3.5 = 35

Fourth bar (165-170) = 5 × 3.6 = 18

Fifth bar (170-180) = 10 × 2.2 -= 22

Seventh bar (190-210) = 20 × 0.6 = 12

(b) Height of third bar = 20 ÷ 5 = 4

Height of sixth bar = 12 ÷ 10 = 1.2

14)

For the “20 < t ≤ 35” class, the frequency density is 225 ÷ 15 = 15.

So the scale on the vertical axis is 10 small divisions to 5 units.

(a) For “10 < t ≤ 20”, frequency = 45 × 10 = 450

For “35 < t ≤ 60”, frequency = 7 × 25 = 175

For “60 < t ≤ 90”, frequency = 3 × 30 = 90

(b) For “0 < t ≤ 5”, frequency density = 40 ÷ 5 = 8

For “5 < t ≤ 10”, frequency density = 150 ÷ 5 = 30

For “90 < t ≤ 150”, frequency density = 60 ÷ 60 = 1

Histograms Worksheet Page 2