Question

for each given standard deviation, enter the letter of the corresponding data set.
= 0
= 0.7071
a
= 2.278
b
= 11.18
c
= 26.926
d
e
done

Explanation:

Step1: Calculate mean of Set A

Data set A: {20,20,20,20}
Mean $\bar{x}_A = \frac{20+20+20+20}{4} = 20$

Step2: Calculate std dev of Set A

Standard deviation $\sigma_A = \sqrt{\frac{\sum(x_i-\bar{x})^2}{n}} = \sqrt{\frac{(20-20)^2+(20-20)^2+(20-20)^2+(20-20)^2}{4}} = \sqrt{0} = 0$

Step3: Calculate mean of Set C

Data set C: {20,19,19,18}
Mean $\bar{x}_C = \frac{20+19+19+18}{4} = 19$

Step4: Calculate std dev of Set C

$\sigma_C = \sqrt{\frac{(20-19)^2+(19-19)^2+(19-19)^2+(18-19)^2}{4}} = \sqrt{\frac{1+0+0+1}{4}} = \sqrt{0.5} \approx 0.7071$

Step5: Calculate mean of Set D

Data set D: {20,19,24,18}
Mean $\bar{x}_D = \frac{20+19+24+18}{4} = 20.25$

Step6: Calculate std dev of Set D

$\sigma_D = \sqrt{\frac{(20-20.25)^2+(19-20.25)^2+(24-20.25)^2+(18-20.25)^2}{4}} = \sqrt{\frac{0.0625+1.5625+14.0625+5.0625}{4}} = \sqrt{\frac{20.75}{4}} \approx 2.278$

Step7: Calculate mean of Set B

Data set B: {20,40,10,30}
Mean $\bar{x}_B = \frac{20+40+10+30}{4} = 25$

Step8: Calculate std dev of Set B

$\sigma_B = \sqrt{\frac{(20-25)^2+(40-25)^2+(10-25)^2+(30-25)^2}{4}} = \sqrt{\frac{25+225+225+25}{4}} = \sqrt{\frac{500}{4}} = \sqrt{125} \approx 11.18$

Step9: Calculate mean of Set E

Data set E: {20,10,30,80}
Mean $\bar{x}_E = \frac{20+10+30+80}{4} = 35$

Step10: Calculate std dev of Set E

$\sigma_E = \sqrt{\frac{(20-35)^2+(10-35)^2+(30-35)^2+(80-35)^2}{4}} = \sqrt{\frac{225+625+25+2025}{4}} = \sqrt{\frac{2900}{4}} = \sqrt{725} \approx 26.926$

Answer:

$0$ = A
$0.7071$ = C
$2.278$ = D
$11.18$ = B
$26.926$ = E