A+ Answers

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