Question

1. Five students visiting the student health center for a free dental work were asked how many months had passed since their last dentist visits. The results were: 6, 17, 11, 22, 29
   1. Calculate, by hand, the variance of the data set. I suggest using the table format.   
   2. What is the numerical value of the standard deviation?
   3. Interpret the standard deviation in terms of the problem

Answer 1

Calculate, by hand, the variance of the data set. I suggest using the table format.   

Solution:

The formulas for mean, variance, and standard deviation for sample are given as below:

Sample Mean = X̄ = ∑ X/n

Sample Variance = S2 = ∑[ (X - mean)^2]/(n - 1)

Sample Standard deviation = S = Sqrt(S2) = Sqrt(Variance)

The calculation table is given as below:

No.	x	(X - mean)^2
1	6	121
2	17	0
3	11	36
4	22	25
5	29	144
Total	85	326

From above table, we have

n = 5

Sample Mean = X̄ = 85/5 = 17

Sample Variance = S2 = 326/(5 - 1) = 326/4 = 81.5

Sample variance = 81.5

What is the numerical value of the standard deviation?

Sample Standard deviation = S = Sqrt(81.5) = 9.027735043

Sample Standard deviation = 9.027735043

Interpret the standard deviation in terms of the problem

The last dentist visit by a student is deviate about by 9 months from the mean.