To determine the first error in computing the standard deviation, let's analyze the provided steps carefully.
1. Identify data points and compute mean:
- Data points: [tex]\(12, 14, 9, 21\)[/tex]
- Mean ([tex]\(\mu\)[/tex]): [tex]\(14\)[/tex]
2. Compute the differences between each data point and the mean:
- [tex]\( 12 - 14 = -2 \)[/tex]
- [tex]\( 14 - 14 = 0 \)[/tex]
- [tex]\( 9 - 14 = -5 \)[/tex]
- [tex]\( 21 - 14 = 7 \)[/tex]
3. Square each of these differences:
- [tex]\((-2)^2 = 4\)[/tex]
- [tex]\(0^2 = 0\)[/tex]
- [tex]\((-5)^2 = 25\)[/tex]
- [tex]\(7^2 = 49\)[/tex]
4. Sum up the squared differences:
- [tex]\(4 + 0 + 25 + 49 = 78\)[/tex]
5. Compute the variance by dividing the sum of squared differences by the number of data points:
- Variance = [tex]\(\frac{78}{4}\)[/tex]
- Standard deviation [tex]\(s = \sqrt{19.5}\)[/tex]
The main point to note here is that Yuri divided by 4 rather than [tex]\(n-1\)[/tex] (which should be 3 in this case since there are 4 data points).
By comparing this step-by-step analysis with the possible errors given:
1. Yuri correctly found the differences between each data point and the mean.
2. Yuri correctly subtracted [tex]\(9 - 14\)[/tex].
3. Yuri correctly squared [tex]\(-2\)[/tex].
The first error made by Yuri is that he divided by [tex]\(n\)[/tex] (which is 4) instead of [tex]\(n - 1\)[/tex] (which is 3).
Therefore, the error is:
Yuri divided by [tex]\(n\)[/tex] instead of [tex]\(n-1\)[/tex].
