find the variance of Q of the following scores in an exam: 92 95 85 75 by using a table to calculate
To find the variance of scores in an exam by using a table, first, list the scores in ascending order:
75, 85, 92, 95
Next, calculate the mean (average) of the scores:
Mean (μ) = (75 + 85 + 92 + 95) / 4 = 347 / 4 = 86.75
Then, subtract the mean from each score, square the differences, and sum them up:
(75 - 86.75)² + (85 - 86.75)² + (92 - 86.75)² + (95 - 86.75)² = 109.5625 + 2.8125 + 31.890625 + 70.5625 = 214.828125
Finally, divide the sum by the total number of scores minus 1 (n-1) to find the variance:
Variance (σ²) = 214.828125 / (4 - 1) = 214.828125 / 3 = 71.609375
Therefore, the variance of the scores is 71.609375.