1.what is the standard deviation of these values
first 7:57,61,57,57,58,57,61 and
second 7:61,52,69,64,46,54,47
2. compare the two sets and describe what you discover.
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 values, you need to follow these steps:
1. Calculate the mean (average) of the set.
2. Subtract the mean from each value in the set.
3. Square each of the differences obtained in step 2.
4. Calculate the mean of the values obtained in step 3.
5. Take the square root of the value obtained in step 4.
Now let's find the standard deviation for the two sets you provided:
First set: 57, 61, 57, 57, 58, 57, 61
1. Calculate the mean:
Mean = (57 + 61 + 57 + 57 + 58 + 57 + 61) / 7 = 408 / 7 ≈ 58.286
2. Subtract the mean from each value:
57 - 58.286 = -1.286
61 - 58.286 = 2.714
57 - 58.286 = -1.286
57 - 58.286 = -1.286
58 - 58.286 = -0.286
57 - 58.286 = -1.286
61 - 58.286 = 2.714
3. Square each difference:
(-1.286)^2 ≈ 1.653
(2.714)^2 ≈ 7.368
(-1.286)^2 ≈ 1.653
(-1.286)^2 ≈ 1.653
(-0.286)^2 ≈ 0.082
(-1.286)^2 ≈ 1.653
(2.714)^2 ≈ 7.368
4. Calculate the mean of the squared differences:
Mean = (1.653 + 7.368 + 1.653 + 1.653 + 0.082 + 1.653 + 7.368) / 7 = 21.43 / 7 ≈ 3.061
5. Take the square root of the mean:
Standard Deviation = √3.061 ≈ 1.749
Second set: 61, 52, 69, 64, 46, 54, 47
Using the same steps above, we find the standard deviation to be ≈ 7.496.
Now, let's compare the two sets' standard deviations:
- The standard deviation of the first set (≈ 1.749) is significantly lower than that of the second set (≈ 7.496).
- This indicates that the values in the first set are less spread out (more clustered around the mean) compared to the values in the second set.
- In other words, the first set displays less variability or dispersion in comparison to the second set.