Find the standard deviation for the given data. Round your answer to one more decimal place than original data.
2,5,47,11,13,48,39,36
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.
To find the standard deviation for the given data, you'll need to follow these steps:
Step 1: Find the mean (average) of the data.
Add all the numbers together: 2 + 5 + 47 + 11 + 13 + 48 + 39 + 36 = 201.
Divide the total by the number of data points: 201 / 8 = 25.125.
Step 2: Subtract the mean from each data point, and square the result.
For each number, subtract the mean (25.125) and square the result.
(2 - 25.125)^2 = 529.531625
(5 - 25.125)^2 = 406.859125
(47 - 25.125)^2 = 472.995625
(11 - 25.125)^2 = 201.581625
(13 - 25.125)^2 = 147.628625
(48 - 25.125)^2 = 522.172625
(39 - 25.125)^2 = 192.348625
(36 - 25.125)^2 = 118.681625
Step 3: Find the average of the squared differences.
Add up all the squared differences and divide by the number of data points.
(529.531625 + 406.859125 + 472.995625 + 201.581625 + 147.628625 + 522.172625 + 192.348625 + 118.681625) / 8 = 286.127875.
Step 4: Take the square root of the average.
The square root of 286.127875 is approximately 16.92.
Step 5: Round the answer to one more decimal place than the original data.
Since the original data is given to one decimal place, round the standard deviation to two decimal places.
Therefore, the standard deviation for the given data is approximately 16.92.