Question

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

x	f
14	1
13	2
12	3
11	5
10	4

c. $sum x^2$

Explanation:

Step1: Calculate \( X^2 \) for each \( X \)

For \( X = 15 \), \( X^2 = 15^2 = 225 \), multiply by \( f = 1 \): \( 225\times1 = 225 \)
For \( X = 14 \), \( X^2 = 14^2 = 196 \), multiply by \( f = 1 \): \( 196\times1 = 196 \)
For \( X = 13 \), \( X^2 = 13^2 = 169 \), multiply by \( f = 2 \): \( 169\times2 = 338 \)
For \( X = 12 \), \( X^2 = 12^2 = 144 \), multiply by \( f = 3 \): \( 144\times3 = 432 \)
For \( X = 11 \), \( X^2 = 11^2 = 121 \), multiply by \( f = 5 \): \( 121\times5 = 605 \)
For \( X = 10 \), \( X^2 = 10^2 = 100 \), multiply by \( f = 4 \): \( 100\times4 = 400 \)

Step2: Sum all the results

Sum \( = 225 + 196 + 338 + 432 + 605 + 400 \)
First, \( 225 + 196 = 421 \)
Then, \( 421 + 338 = 759 \)
Then, \( 759 + 432 = 1191 \)
Then, \( 1191 + 605 = 1796 \)
Then, \( 1796 + 400 = 2196 \)

Answer:

\( 2196 \)