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for the question they handed over — — compute the population variance on April 1st, assuming the following data points: 10, 15, 20, 25, 30. Thanks,
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The problem requires calculating the population variance for the given data set: 10, 15, 20, 25, 30. To compute the population variance, I first need to find the mean of the data set. The mean is computed as (10 + 15 + 20 + 25 + 30)/5 = 20. Next, I calculate the squared differences from the mean for each data point:
(10 – 20)^2 = 100
(15 – 20)^2 = 25
(20 – 20)^2 = 0
(25 – 20)^2 = 25
(30 – 20)^2 = 100
Summing these squared differences gives a total of 100 + 25 + 0 + 25 + 100 = 250. To find the population variance, I divide this sum by the number of data points, which is 5: 250/5 = 50. Therefore, the population variance for this data set is 50.
Finally, consider the use case where we want to understand the variability or spread of the data around the mean, and a variance of 50 indicates moderate dispersion. Hence, the computed population variance is 50.
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