For the following distribution of scores,SX = 18.? $$\begin{array} { l l }
X & f \
4 & 1 \
3 & 2 \
2 & 3 \
1 & 2 \
\hline
\end{array}$$

Question

For the following distribution of scores,SX = 18.? $$\begin{array} { l l } 
X & f \
4 & 1 \
3 & 2 \
2 & 3 \
1 & 2 \
\hline
\end{array}$$

Quizplus · Accepted Answer

To find SX, we need to first find the mean, which is:

mean = Σ(X * f) / Σf
      = (4*1 + 3*2 + 2*3 + 1*2) / (1+2+3+2)
      = 16/8
      = 2

Next, we need to find the sum of squared deviations from the mean, which is:

Σ(X - mean)^2 * f
= (4-2)^2*1 + (3-2)^2*2 + (2-2)^2*3 + (1-2)^2*2
= 2 + 2 + 0 + 2
= 6

Finally, we can calculate SX using the formula:

SX = √(Σ(X - mean)^2 * f / N)
   = √(6/8)
   = 0.866

Therefore, the statement is true.

For the Following Distribution of Scores,SX = 18 Xf41322312\begin{array} { l l } X & f \\4 & 1 \\3 & 2 \\2 & 3 \\1 & 2 \\\hline\end{array}X4321​f1232​​