Statistics
QUESTION 1 a) Construct a “less than or equal” cumulative frequency polygon for Table 1.
Table 1
Class Class Midpoint Frequency Cumulative Frequency
6 – 8 7 4 4
9 – 11 10 6 4 + 6 = 10
12 – 14 13 10 10 + 10 = 20
15 – 17 16 3 20 + 3 = 23
18 – 20 19 12 23 + 12 = 35
b) Based on Table 2, construct a frequency distribution table. Take 10 as a class width and 50 as a lower limit.
Table 2
51 64 76 52 84 72 60 56 88 56
64 72 60 64 76 56 68 84 57 60
88 60 86 60 84 68 60 72 64 64
72 88 72 64 88 60 60 84 68 72
QUESTION 2 Complete the Table 3 and calculate the mean, mode and standard deviation.
Table 3
Class/Kelas Midpoint/ Titik Tengah f f x f x2
1.8 – 2.5 2.15 2 4.3 9.245
2.6 – 3.3 2.95 4 11.8 34.81
3.4 – 4.1 3.75 6 22.5 84.375
4.2 – 4.9 4.55 13 59.15 269.1325
5.0 – 5.7 5.35 8 42.8 228.98
5.8 – 6.5 6.15 3 18.45 113.4675
QUESTION 3 Based on the data in Table 4,
a) construct a frequency distribution.
b) calculate mean, mode and median.
Table 4
8.0 12.9 13.0 8.9 10.1 17.3 11.1 10.9 6.2 8.1 8.8 10.4 15.7 13.6 19.3 9.9 8.5 11.1 10.7 8.8 10.7 6.8 7.4 4.8 11.8 13.0 9.5 8.1 6.9 11.5 11.2 13.6 4.9 18.8 15.7 10.8 10.7 11.5 16.1 9.9
QUESTION 4
Table 5
Class Frequency Frequency Cum. Frequency
40 – 44 2 2 2
45 – 49 x 4 6
50 – 54 7 7 13
55 – 59 4x 16 29
60 – 64 5x 20 49
65 – 69 2 2 51
70 – 74 1 1 52
Given that the total frequency is 52. Based on Table 5, determine:
a) the value of x
b) first quartile
c) median
d) third quartile
e) inter-quartile range
