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).
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I've posted this question earlier and I'm still getting the wrong answer.
I don't know from what point I messed up.....
this is what I did.
Mean:
90+320+770+360+100 / 24 = 68.33
Deviation
469.59+136.19+2.79+69.39+335.99 / 24= 42.25
then square root of 42.45 is 6.5
but my answer came wrong. please help!
I can't move on to my next homework question because I keep getting this wrong :(
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.
For example, with the score of 80:
(80-68.33)^2 * 4 = 136.19 * 4 = ?
Do this with all the frequencies.
To calculate the standard deviation for a set of data, you need to follow these steps:
1. Find the mean (average) of the data set. It seems like you calculated the mean correctly as 68.33. Great job!
2. Calculate the deviation for each data point from the mean. To do this, subtract the mean from each data point.
Using your example:
Deviations: 90-68.33 = 21.67
80-68.33 = 11.67
70-68.33 = 1.67
60-68.33 = -8.33
50-68.33 = -18.33
3. Square each deviation to eliminate negative values and emphasize larger deviations.
Using your example:
Squared Deviations: 21.67^2 ≈ 470.2089
11.67^2 ≈ 136.4889
1.67^2 ≈ 2.7889
(-8.33)^2 ≈ 69.3289
(-18.33)^2 ≈ 335.4889
4. Multiply each squared deviation by its corresponding frequency (number of occurrences).
Using your example:
Frequency: 1, 4, 11, 6, 2
Weighted Squared Deviations:
For 21.67: 1 * 470.2089 = 470.2089
For 11.67: 4 * 136.4889 = 545.9556
For 1.67: 11 * 2.7889 = 30.6789
For -8.33: 6 * 69.3289 = 415.9734
For -18.33: 2 * 335.4889 = 670.9778
5. Calculate the sum of the weighted squared deviations.
Using your example:
Sum of Weighted Squared Deviations:
470.2089 + 545.9556 + 30.6789 + 415.9734 + 670.9778 = 2133.7946
6. Calculate the variance by dividing the sum of the weighted squared deviations by the total number of data points. In this case, the total number of data points is the sum of the frequencies.
Using your example:
Variance = 2133.7946 / 24 = 88.908
7. Finally, take the square root of the variance to find the standard deviation.
Using your example:
Standard Deviation ≈ √88.908 ≈ 9.43
So, the standard deviation for the given data set is approximately 9.43, rounded to the nearest hundredth.