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 :(

looks like you weighted the values for the mean, but not for the deviation.

To find the correct standard deviation, you need to follow a specific formula that takes into account the frequency of each test score. It seems like you've made a mistake in calculating the deviations.

Let's go through the steps again to find the standard deviation:

1. Calculate the mean (average):
To find the mean of the test scores, you need to multiply each score by its respective frequency and sum them up. Then, divide the sum by the total frequency.
Mean = (90 * 1) + (80 * 4) + (70 * 11) + (60 * 6) + (50 * 2) / (1 + 4 + 11 + 6 + 2) = 64.4 (rounded to one decimal place).

2. Calculate the deviations from the mean for each test score:
To calculate the deviation for each test score, subtract the mean from each score.
Deviations: 90 - 64.4 = 25.6, 80 - 64.4 = 15.6, 70 - 64.4 = 5.6, 60 - 64.4 = -4.4, 50 - 64.4 = -14.4.

3. Square each deviation:
Square each deviation to eliminate the negative signs:
25.6^2 = 655.36, 15.6^2 = 243.36, 5.6^2 = 31.36, (-4.4)^2 = 19.36, (-14.4)^2 = 207.36.

4. Multiply each squared deviation by its respective frequency:
Multiply each squared deviation by its corresponding frequency:
655.36 * 1 = 655.36, 243.36 * 4 = 973.44, 31.36 * 11 = 344.96, 19.36 * 6 = 116.16, 207.36 * 2 = 414.72.

5. Calculate the sum of the squared deviations:
Sum up all the products obtained in the previous step:
655.36 + 973.44 + 344.96 + 116.16 + 414.72 = 2504.64.

6. Calculate the variance:
To find the variance, divide the sum of squared deviations obtained above by the total frequency minus 1:
Variance = 2504.64 / (24 - 1) = 107.99 (rounded to two decimal places).

7. Calculate the standard deviation:
Finally, take the square root of the variance calculated in the previous step to find the standard deviation:
Standard deviation = √107.99 = 10.39 (rounded to two decimal places).

Therefore, the correct standard deviation for the test scores is 10.39.