what is the standard deviation if 12 randomly chosen students were asked how many times they had missed class during a certain semester with this result 2,1,5,1,1,3,4,3,1,1,5,1,8.

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 of a set of data, you need to follow these steps:

1. Find the mean (average) of the data set.
2. Subtract the mean from each data point and square the result.
3. Find the mean of the squared differences.
4. Take the square root of the mean from step 3.

Let's apply these steps to the given data set:

Step 1: Find the mean
To find the mean, add up all the numbers and divide the sum by the total number of data points.

2 + 1 + 5 + 1 + 1 + 3 + 4 + 3 + 1 + 1 + 5 + 1 + 8 = 36

The total sum is 36.
Since there are 12 data points, divide the sum by 12.

Mean = 36 / 12 = 3

The mean is 3.

Step 2: Subtract the mean and square the result

Subtract the mean (3) from each data point and square the results.

(2 - 3)^2 = 1
(1 - 3)^2 = 4
(5 - 3)^2 = 4
(1 - 3)^2 = 4
(1 - 3)^2 = 4
(3 - 3)^2 = 0
(4 - 3)^2 = 1
(3 - 3)^2 = 0
(1 - 3)^2 = 4
(1 - 3)^2 = 4
(5 - 3)^2 = 4
(1 - 3)^2 = 4
(8 - 3)^2 = 25

Step 3: Find the mean of the squared differences

Add up all the squared differences and divide by the total number of data points (12 in this case).

1 + 4 + 4 + 4 + 4 + 0 + 1 + 0 + 4 + 4 + 4 + 25 = 55

Mean = 55 / 12 ≈ 4.58

Step 4: Take the square root

Take the square root of the mean from step 3.

√(4.58) ≈ 2.14

So, the standard deviation of the given data set is approximately 2.14.