Question

please calculate the sd of a sample of 6 data points using the formula taught in class and provided in the formula sheet. the information is below.
the mean of the sample is 5.9. the sum of all the scores squared ($\sum x^2$) is 5960. include 2 decimal places.
a. 43.92
b. 33.92
c. 30.96
d. 1150.23

Explanation:

Step1: Recall sample SD formula

Sample standard deviation formula:
$$s = \sqrt{\frac{\sum X^2 - \frac{(\sum X)^2}{n}}{n-1}}$$
First, calculate $\sum X$ using $\bar{X} = \frac{\sum X}{n}$, so $\sum X = \bar{X} \times n$

Step2: Calculate sum of data points

$\sum X = 5.9 \times 6 = 35.4$

Step3: Compute numerator inside sqrt

$$\sum X^2 - \frac{(\sum X)^2}{n} = 5960 - \frac{(35.4)^2}{6}$$
$$= 5960 - \frac{1253.16}{6} = 5960 - 208.86 = 5751.14$$

Step4: Divide by degrees of freedom

$$\frac{5751.14}{6-1} = \frac{5751.14}{5} = 1150.228$$

Step5: Take square root

$$s = \sqrt{1150.228} \approx 33.92$$

Answer:

b. 33.92