Question

1. using the following informal histogram, calculate each of the following.

a. (n)
b. (sum x)
c. (sum x^{2})

1. based on the following absolute frequency table, calculate each of the followin

Explanation:

Step1: Calculate n (total number of data - points)

Sum the frequencies. $n=1 + 2+3+3+4+2+1=16$

Step2: Calculate $\sum X$ (sum of all data - points)

Multiply each $x$ - value by its frequency and sum. $\sum X=(1\times1)+(2\times2)+(3\times3)+(4\times3)+(5\times4)+(6\times2)+(7\times1)=1 + 4+9+12+20+12+7 = 65$

Step3: Calculate $\sum X^{2}$

Multiply each $x^{2}$ - value by its frequency and sum. $\sum X^{2}=(1^{2}\times1)+(2^{2}\times2)+(3^{2}\times3)+(4^{2}\times3)+(5^{2}\times4)+(6^{2}\times2)+(7^{2}\times1)=1+8 + 27+48+100+72+49 = 305$

Answer:

a. $n = 16$
b. $\sum X=65$
c. $\sum X^{2}=305$