Question

below are the scores for 21 participants. calculate (using excel) both the mean and sd, and enter the larger statistic of the two.
8 1 2
4 5 2
6 2 1
2 4 1
1 2 3
3 3 4
1 2 2

Explanation:

Step1: List all 21 scores

Scores: $8, 1, 2, 4, 5, 2, 6, 2, 1, 2, 4, 1, 1, 2, 3, 3, 3, 4, 1, 2, 2$

Step2: Calculate the mean

Sum all scores, divide by 21.
$\text{Mean} = \frac{8+1+2+4+5+2+6+2+1+2+4+1+1+2+3+3+3+4+1+2+2}{21} = \frac{65}{21} \approx 3.095$

Step3: Calculate sample standard deviation

Use sample SD formula: $s = \sqrt{\frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n-1}}$
First compute squared deviations, sum them:
$\sum(x_i - \bar{x})^2 \approx (8-3.095)^2 + (1-3.095)^2 + ... + (2-3.095)^2 \approx 72.8095$
Then:
$s = \sqrt{\frac{72.8095}{21-1}} = \sqrt{3.6405} \approx 1.908$

Step4: Compare mean and SD

$3.095 > 1.908$

Answer:

$\approx 3.10$ (or exact value $\frac{65}{21}$)