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.
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.
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Correct Answer: Option
Explanation:
(a)
Frequency Distribution Table
(b)
(c) Modal class is 75 - 84
Mode = \(\frac{75 + 84}{2} = 79.5\)
(d)
Mean \(\bar{x} = \frac{\sum fx}{\sum f}\)
= \(\frac{3915}{50}\)
= \(78.3\).
(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)
(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 \(\bar{x} = \frac{\sum fx}{\sum f}\)
= \(\frac{3915}{50}\)
= \(78.3\).