Score Percent of Students
5 13.6
4 22.9
3 25.4
2 18.9
1 19.2
find the mean and standard deviation of the scores
To find the mean and standard deviation of the scores, follow these steps:
Step 1: Calculate the product of each score and its corresponding percentage.
Score * Percent = (Score * Percent)
5 * 13.6 = 68
4 * 22.9 = 91.6
3 * 25.4 = 76.2
2 * 18.9 = 37.8
1 * 19.2 = 19.2
Step 2: Calculate the sum of all the products obtained in step 1.
Sum of products = 68 + 91.6 + 76.2 + 37.8 + 19.2 = 293.8
Step 3: Calculate the sum of all the percentages.
Sum of percentages = 13.6 + 22.9 + 25.4 + 18.9 + 19.2 = 100
Step 4: Calculate the mean.
Mean = Sum of products / Sum of percentages
Mean = 293.8 / 100 = 2.938
Step 5: Calculate the squared difference between each score and the mean.
Score - Mean = (Score - Mean)
5 - 2.938 = 2.062
4 - 2.938 = 1.062
3 - 2.938 = 0.062
2 - 2.938 = -0.938
1 - 2.938 = -1.938
Step 6: Square each value obtained in step 5.
(2.062)^2 = 4.25
(1.062)^2 = 1.13
(0.062)^2 = 0.004
(-0.938)^2 = 0.88
(-1.938)^2 = 3.75
Step 7: Calculate the sum of all the squared differences obtained in step 6.
Sum of squared differences = 4.25 + 1.13 + 0.004 + 0.88 + 3.75 = 10.014
Step 8: Calculate the variance.
Variance = Sum of squared differences / Number of scores
Variance = 10.014 / 5 = 2.0028
Step 9: Calculate the standard deviation.
Standard deviation = Square root of the variance
Standard deviation = √2.0028 = 1.414
Therefore, the mean of the scores is approximately 2.938 and the standard deviation is approximately 1.414.