Consider the following test scores obtained by a class.

Test score

90

80

70

60

50

Frequency

1

4

11

6

2

Find the standard deviation (rounded to the nearest hundredth).

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, you can follow these steps:

Step 1: Find the mean (average) of the data set.

To find the mean, you need to sum up all the test scores and divide by the total frequency.

Mean = (90*1 + 80*4 + 70*11 + 60*6 + 50*2) / (1 + 4 + 11 + 6 + 2)

= (90 + 320 + 770 + 360 + 100) / 24

= 1640 / 24

≈ 68.33

So, the mean is approximately 68.33.

Step 2: Find the squared deviation from the mean for each data point.

Subtract the mean from each test score and square the result.

Squared Deviation = (Test score - Mean)^2

For example, for the first test score:

Squared Deviation = (90 - 68.33)^2 ≈ 477.51

Repeat this calculation for each test score.

Step 3: Calculate the sum of the squared deviations.

Sum up all the squared deviations.

Sum of Squares = (1 * 477.51) + (4 * squared deviation for 80) + (11 * squared deviation for 70) + (6 * squared deviation for 60) + (2 * squared deviation for 50)

Step 4: Calculate the variance.

Variance = Sum of Squares / Total Frequency

So, for our example:

Variance = Sum of Squares / Total Frequency

= 4860.51 / 24

≈ 202.52

Step 5: Calculate the standard deviation.

The standard deviation is the square root of the variance.

Standard Deviation = √Variance

So, for our example:

Standard Deviation ≈ √202.52

≈ 14.24

Therefore, the standard deviation of the given test scores, rounded to the nearest hundredth, is approximately 14.24.