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.
Explanation
(a)
| 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 \(\bar{x} = \frac{\sum fx}{\sum f}\)
= \(\frac{3915}{50}\)
= \(78.3\).