Question

question 23
find each value requested for the set of scores in the following frequency - distribution table.
a. n
b. σx
c. σx²
x f
5 3
4 4
3 2
2 1
1 3

Explanation:

Step1: Calculate N (total number of scores)

Sum the frequencies. $N=3 + 4+2 + 1+3=13$

Step2: Calculate $\sum X$ (sum of scores weighted by frequency)

Multiply each $X$ - value by its frequency and sum. $\sum X=(5\times3)+(4\times4)+(3\times2)+(2\times1)+(1\times3)=15 + 16+6 + 2+3=42$

Step3: Calculate $\sum X^{2}$ (sum of squared - scores weighted by frequency)

First square each $X$ - value, then multiply by its frequency and sum. $\sum X^{2}=(5^{2}\times3)+(4^{2}\times4)+(3^{2}\times2)+(2^{2}\times1)+(1^{2}\times3)=(25\times3)+(16\times4)+(9\times2)+(4\times1)+(1\times3)=75+64 + 18+4 + 3=164$

Answer:

a. $N = 13$
b. $\sum X=42$
c. $\sum X^{2}=164$