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Answer :
Final answer:
The range of the data set is 32.9. The sample Statistics deviation and population variance are calculated by first finding the mean of the dataset. This mean is used to find the squared difference from the mean for each datum, which are then used to calculate the variance and standard deviation.
Explanation:
The given data set is: 10.3, 22, 38.5, 43.2 where the respective frequencies are 7, 12, 5, and 2.
The range is the difference between the maximum and minimum values, which is 43.2 - 10.3 = 32.9.
To calculate the sample standard deviation and the population variance, first, we need to find the mean of the dataset. Each datum is multiplied by its frequency, these products are then summed and divided by the total number of data points.
Once the mean (µ) is calculated, find the squared difference from the mean for each datum, multiply each squared difference by the respective frequency, and sum these values together.
To get the population variance, divide by the total number of data points. The square root of this value results in the population standard deviation. In contrast, for the sample standard deviation, divide by the total number of data points minus 1 before taking the square root.
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