Find the sum of the squares of the deviations from the mean of a series of ACT scores: 24,17,27,25,22
well, what's the mean µ?
Just add up (24-µ)^2 + ... + (22-µ)^2
To find the sum of the squares of the deviations from the mean of a series of scores, we need to follow a few steps:
Step 1: Find the mean of the series.
Step 2: Calculate the deviation from the mean for each score.
Step 3: Square each deviation.
Step 4: Add up all the squared deviations.
Let's go through these steps to find the answer.
Step 1: Find the mean
To find the mean of the given series of ACT scores (24, 17, 27, 25, 22), add up all the scores and divide the sum by the number of scores.
Mean = (24 + 17 + 27 + 25 + 22) / 5
Mean = 115 / 5
Mean = 23
Step 2: Calculate the deviation from the mean
For each score, subtract the mean from the score to find the deviation.
Deviation from mean = Score - Mean
For example:
- Deviation from mean for the first score (24) = 24 - 23 = 1
- Deviation from mean for the second score (17) = 17 - 23 = -6
- Deviation from mean for the third score (27) = 27 - 23 = 4
- Deviation from mean for the fourth score (25) = 25 - 23 = 2
- Deviation from mean for the fifth score (22) = 22 - 23 = -1
Step 3: Square each deviation
Take each deviation found in Step 2 and square it.
For example:
- Squaring the deviation of 1: 1^2 = 1
- Squaring the deviation of -6: (-6)^2 = 36
- Squaring the deviation of 4: 4^2 = 16
- Squaring the deviation of 2: 2^2 = 4
- Squaring the deviation of -1: (-1)^2 = 1
Step 4: Add up all the squared deviations
Finally, add up all the squared deviations to get the sum of the squares of the deviations from the mean.
Sum of squared deviations = 1 + 36 + 16 + 4 + 1 = 58
So, the sum of the squares of the deviations from the mean of the given series of ACT scores (24, 17, 27, 25, 22) is 58.