Answer :
The median of the given distribution is 497.5.
To calculate the median of a distribution using a histogram, follow these steps:
1. Identify the class interval that contains the median. In this case, the class interval with the highest frequency is the interval between 24.5 and 35.5.
2. Find the cumulative frequency of the class interval below the median. To do this, add up the frequencies of all the intervals that come before the median interval. In this case, the cumulative frequency of the interval below the median is 7.
3. Determine the total frequency of the distribution. Add up all the frequencies in the histogram. In this case, the total frequency is 100.
4. Use the formula: Median = L + [(N/2 - CF) * C], where L is the lower boundary of the median interval, N is the total frequency, CF is the cumulative frequency below the median, and C is the class width.
5. Plug in the values: L = 24.5, N = 100, CF = 7, and C = 11 (35.5 - 24.5).
6. Calculate the median using the formula: Median = 24.5 + [(100/2 - 7) * 11]. This simplifies to Median = 24.5 + [(50 - 7) * 11].
7. Calculate the final value of the median: Median = 24.5 + (43 * 11). This gives us Median = 24.5 + 473.
The median of the given distribution is 497.5.
To calculate the median of a distribution using a histogram, find the class interval with the highest frequency. Then, determine the cumulative frequency of the interval below the median and the total frequency of the distribution.
Use the formula Median = L + [(N/2 - CF) * C], where L is the lower boundary of the median interval, N is the total frequency, CF is the cumulative frequency below the median, and C is the class width. Plug in the values and calculate. In this case, the median is 497.5.
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