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Calculate the median given the following data:

Mid-value: 20, 30, 40, 50, 60, 70

Male (c.f.): 12, 25, 42, 46, 48, 50

Note: c.f. = Cumulative Frequency

Answer :

Final answer:

The median is found by determining the mid-point in the cumulative frequency data, which in this case is the 25th position. The corresponding mid-value for this position is 30, thus the median for the given data is 30.

Explanation:

Calculating the Median from Cumulative Frequency Data

To find the median in a set of data represented by a cumulative frequency table, first, identify the total number of data points, which is the last value in the cumulative frequency column. For this dataset, the total number of males is 50.

Since the median is the middle value, divide the total number of data points by 2 to find the position of the median in the dataset. In this case, 50 / 2 = 25, so the median will be the 25th value.

Next, look at the cumulative frequencies to determine which mid-value corresponds to the median. Since the cumulative frequency just before reaching 25 is 25 at the 30 mid-value, and the next cumulative frequency is 42 at the 40 mid-value, the median lies within the 30 mid-value group. Thus, the median is 30.

To summarize, we found the position of the median in the cumulative frequency column (25th position) and then identified the corresponding mid-value as the median, which in this case is 30.

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