Question

multiple choice 10 points
for the following frequency distribution, what is the value of σx²?
x f
4 1
3 0
2 2
1 1
10
25
100
none of the above

Explanation:

Step1: Calculate $X^{2}$ for each row

For $X = 4$, $X^{2}=4^{2}=16$; for $X = 3$, $X^{2}=3^{2}=9$; for $X = 2$, $X^{2}=2^{2}=4$; for $X = 1$, $X^{2}=1^{2}=1$.

Step2: Multiply by frequency and sum

For $X = 4,f = 1$, product is $16\times1 = 16$; for $X = 3,f = 0$, product is $9\times0 = 0$; for $X = 2,f = 2$, product is $4\times2=8$; for $X = 1,f = 1$, product is $1\times1 = 1$. Then $\sum X^{2}=16 + 0+8 + 1=25$.

Answer:

25