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Question

The following table gives the frequency distribution of married women by age at marriage: Age (in years) Frequency Age (in years) Frequency 15âˆ’19 20âˆ’24 25âˆ’29 30âˆ’34 35âˆ’39 53 140 98 32 12 40âˆ’44 45âˆ’49 50âˆ’54 55âˆ’59 60 and above 9 5 3 3 2 Calculate the median and interpret the results.

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Solution

Here, the frequency table is given in inclusive form. So, we first transform it into exclusive form by subtracting and adding h/2 to the lower and upper limits respectively of each class, where h denotes the difference of lower limit of a class and upper limit of the previous class. We have, N = 357 So, N/2 = 178.5 Thus, the cumulative frequency just greater than 178.5 is 193 and the corresponding class is 19.5âˆ’24.5. Therefore, 19.5âˆ’24.5 is the median class. Here, l = 19.5, f = 140, F = 193 and h = 5 We know that $=19.5+\left(\frac{178.5-53}{140}\right)Ã—5\phantom{\rule{0ex}{0ex}}=19.5+\frac{125.5}{140}Ã—5\phantom{\rule{0ex}{0ex}}=19.5+\frac{125.5}{28}\phantom{\rule{0ex}{0ex}}=\frac{546+125.5}{28}\phantom{\rule{0ex}{0ex}}=23.98$ Hence, the median age 23.98 years. Thus, nearly half the women were married between the age of 19.5 years and 24.5 years.

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