The number of child births recorded in 50 maternity centres of a local government in August 1993 are as follows :
50 99 81 86 69 85 93 63 92 65 77 74 76 71 90 74 81 94 67 75 95 81 68 105 99 68 75 75 76 73 79 74 80 69 74 62 74 80 79 68 79 75 75 71 83 75 80 85 81 82
(a) Construct a frequency distribution table, using class intervals 45 - 54, 55 - 64, etc.
(b) Draw the histogram for the distribution
(c) Use your histogram to estimate the mode.
(d) Calculate the mean number of births.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
Frequency Distribution Table
Birth
45 - 54
55 - 64
65 - 74
75 - 84
85 - 94
95 - 104
105 - 114
Freq(f)
1
2
15
21
7
3
1
(b) see histogram above.
(c) Modal class is 75 - 84
Mode = \(\frac{75 + 84}{2} = 79.5\)
(d)
Birth
freq (f)
class midpoint
(x)
\(fx\)
45 - 54
1
49.5
49.5
55 - 64
2
59.5
119
65 - 74
15
69.5
1042.5
75 - 84
21
79.5
1669.5
85 - 94
7
89.5
626.5
95 - 104
3
99.5
298.5
105 - 114
1
109.5
109.5
Total
50
3915
Mean \(\bar{x} = \frac{\sum fx}{\sum f}\)
= \(\frac{3915}{50}\)
= \(78.3\).
Source: Myschool Past Questions Archive (Record #53390)