Economy, asked by malaikar4321, 5 hours ago

20. Calculate standard deviation from the following: 1 2 Roll No. 3 4 5 6 7 8 9 10 11 12 Marks 52 43 59 48 78 52 65 48 57 37 31 60

Answers

Answered by Afreenakbar

Answer:

13.8614

Explanation:

To calculate the standard deviation, we first need to find the mean (average) of the data.

Mean = (52 + 43 + 59 + 48 + 78 + 52 + 65 + 48 + 57 + 37 + 31 + 60) / 12 = 51.67

Next, we subtract the mean from each data point and square the result to find the deviation of each data point.

Deviation = (52 - 51.67)^2 = 0.0489

Deviation = (43 - 51.67)^2 = 36.0489

Deviation = (59 - 51.67)^2 = 36.0489

Deviation = (48 - 51.67)^2 = 9.0489

Deviation = (78 - 51.67)^2 = 324.0489

Deviation = (52 - 51.67)^2 = 0.0489

Deviation = (65 - 51.67)^2 = 144.0489

Deviation = (48 - 51.67)^2 = 9.0489

Deviation = (57 - 51.67)^2 = 25.0489

Deviation = (37 - 51.67)^2 = 324.0489

Deviation = (31 - 51.67)^2 = 625.0489

Deviation = (60 - 51.67)^2 = 144.0489

We then add up all the deviations and divide by the number of data points (minus one) to find the variance.

Variance = (0.0489 + 36.0489 + 36.0489 + 9.0489 + 324.0489 + 0.0489 + 144.0489 + 9.0489 + 25.0489 + 324.0489 + 625.0489 + 144.0489) / 11 = 191.3187

Finally, we take the square root of the variance to find the standard deviation.

Standard deviation = √ 191.3187 = 13.8614