Question

103 4.2 Four Measures of Dispersion oschool children, particularly those who are very intelligent, often create imaginary companions. The following data represent the number of compan- ions created by 15 children. 4 2 5 3 1 3 2 1 2 3 2 4 3 2 0 (a) Compute the mean and the standard deviation using the formulas X = 2; -1X/n and S = V (X, - x)2/n. (b) If you have a calcula- tor with a standard deviation key, compute the standard deviation with your calculator

Answer 1

Solution :

a)

X : Number of companions created by 15 children .

The data set is

4,2,5,3,1,3,2,1,2,3,2,4,3,2,0

In order to find Mean and standard deviation , Find sum of all observation first .

Sum of All observation = $\sum Xi$ = 37

Now ,

Mean =

ΣΧί 37 - = = = 2.466666667 = 2.4667

Now substract Mean from each value of X then square that term and all the terms , After taking square root , you will get standard deviation S .

I have created table in Ms-excel .

X-mean	(X-Mean)^2
1.5333	2.35100889
-0.4667	0.21780889
2.5333	6.41760889
0.5333	0.28440889
-1.4667	2.15120889
0.5333	0.28440889
-0.4667	0.21780889
-1.4667	2.15120889
-0.4667	0.21780889
0.5333	0.28440889
-0.4667	0.21780889
1.5333	2.35100889
0.5333	0.28440889
-0.4667	0.21780889
-2.4667	6.08460889
Total->	23.7333334

From table ,

Σ(Xi - X)2 = 23.7333

Thereofore

Σ(Xi - X). 23.7333 1.5822

Now , Standard deviation is given by ,

S-Ven Σ(Xi - X)2 -= V1.5822 = 1.2778

*All value are rounded up to to 4 decimal places .

b) Obviously the answer for standard deviation in calculated is same and it is

1.25786415

After round off S=1.2578 .