Calculate the standard deviation for the following yields of corn: 142, 161, 132, 143, 147, 145, 146, and 152 bu/ac.
Are all yields obtained within one standard deviation of the mean?
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.
Without even calculating the SD, the answer is no. ±1 SD is only about 68% of the scores.