Determine the standard deviation from the mean of the ages of the students in a technical mathematics class whose ages are: 42, 18, 19, 20, 23, 36, 18, 25, 20, 20, 24, 22, 26, 29, 37, 20, 20, 27, 42, 51, 24, 45, 24, 18, 31.
A)27.24
B)20
C)9.52
D)33

Question

Quizplus · Accepted Answer

To find the standard deviation, we need to first find the mean of the ages:

Mean = (42+18+19+20+23+36+18+25+20+20+24+22+26+29+37+20+20+27+42+51+24+45+24+18+31)/25 
Mean = 27.08

Next, we need to find the variance:

Variance = 1/n * ∑(xi - mean)^2

Variance = (1/25) * [(42-27.08)^2 + (18-27.08)^2 + (19-27.08)^2 + (20-27.08)^2 + (23-27.08)^2 + (36-27.08)^2 + (18-27.08)^2 + (25-27.08)^2 + (20-27.08)^2 + (20-27.08)^2 + (24-27.08)^2 + (22-27.08)^2 + (26-27.08)^2 + (29-27.08)^2 + (37-27.08)^2 + (20-27.08)^2 + (20-27.08)^2 + (27-27.08)^2 + (42-27.08)^2 + (51-27.08)^2 + (24-27.08)^2 + (45-27.08)^2 + (24-27.08)^2 + (18-27.08)^2 + (31-27.08)^2]

Variance = 206.1

Finally, we can find the standard deviation by taking the square root of the variance:

Standard deviation = √(variance) = √(206.1) = 9.52

Therefore, the answer is C) 9.52.

Determine the Standard Deviation from the Mean of the Ages