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
time left 0:13:03

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

Mean = $\frac{\text{Sum of all scores}}{\text{Number of scores}}$
Sum = $8+1+2+4+5+2+6+2+1+2+4+1+1+2+3+3+3+4+1+2+2 = 61$
Mean = $\frac{61}{21} \approx 2.9048$

Step3: Calculate sample standard deviation

First, find squared differences from the mean for each score, sum them, divide by $n-1=20$, then take the square root.
Sum of squared differences:
$(8-2.9048)^2 + (1-2.9048)^2 + \dots + (2-2.9048)^2 \approx 77.0952$
Sample SD = $\sqrt{\frac{77.0952}{20}} = \sqrt{3.8548} \approx 1.9634$

Step4: Compare mean and SD

$2.9048 > 1.9634$

Answer:

$2.90$ (rounded to two decimal places, or $2.9048$ for more precision)