What are the mean, variance and standard deviation of these values?
62,41,54,60,49,58.
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
I'll let you do the calculations.
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To find the mean, variance, and standard deviation of a set of values, follow these steps:
Mean:
1. Add up all the values: 62 + 41 + 54 + 60 + 49 + 58 = 324.
2. Divide the sum by the number of values: 324 ÷ 6 = 54.
So, the mean (average) of these values is 54.
Variance:
1. Find the difference between each value and the mean: (62 - 54), (41 - 54), (54 - 54), (60 - 54), (49 - 54), (58 - 54).
2. Square each of the differences: 8², -13², 0², 6², -5², 4².
3. Add up all the squared differences: 64 + 169 + 0 + 36 + 25 + 16 = 310.
4. Divide the sum by the number of values: 310 ÷ 6 = 51.67 (rounded to two decimal places).
Therefore, the variance of these values is approximately 51.67.
Standard Deviation:
1. Take the square root of the variance: √51.67 = 7.19 (rounded to two decimal places).
Hence, the standard deviation of these values is approximately 7.19.