Answer :
The mean of a distribution with the following histogram Frequency is 4.84.
To calculate the mean of a distribution using a histogram, we need to find the midpoint of each class interval and multiply it by its corresponding frequency.
Then, we sum up these products and divide by the total number of data points.
In this case, the class boundaries are as follows:
- 24.55
- 29.45
- 29.48
- 24.57
To find the midpoint of each class, we can add the lower and upper class boundaries and divide by 2:
- Midpoint of the first class = (24.55 + 29.45) / 2 = 27
- Midpoint of the second class = (29.45 + 29.48) / 2 = 29.465
- Midpoint of the third class = (29.48 + 24.57) / 2 = 27.025
Next, we multiply each midpoint by its corresponding frequency:
- (27 * 3) + (29.465 * 1) + (27.025 * 46.5) = 253.06
Finally, we divide the sum by the total number of data points (sum of frequencies):
- 253.06 / (3 + 1 + 46.5) = 4.84 (rounded to two decimal places)
Therefore, the mean of the distribution is approximately 4.84.
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