Answer to Question #318849 in Statistics and Probability for Saad

Question

Question 2:

If the following frequency distribution shows the average number of students per teacher in the 50 major cities of Pakistan

Class Limits

Frequency

9-11

3

12 – 14

5

15 – 17

12

18 – 20

18

21 – 23

8

24 – 26

4

Table 1

Determine

·        Range

·        Mean

·        Median

·        Mode

·        Standard Deviation

·        Relative Dispersion

·        Variance

·        Kurtosis

Answer 1

Range =Max-Min

Range =26-9=17

Mean=$\sum$ fx/$\sum$f

Mean =${905/50}$

Mean =18.1

Median =L+ $\frac{n/2-c}{f}\cdot h$

Median =17.5+$\frac{25-20}{18}\cdot3$ =18.3333

Mode =L+ $\frac{f1-f0}{2f1-fo-f2}\cdot h$

Mode=17.5+$\frac{18-12}{36-12-8} \cdot 3$ =18.625

Standard deviation =$\surd\frac{\sum(Xi-Mean x)^2}{n-1}$

Standard deviation =$\surd \frac{706.5}{49}$ =3.7972

Relative Dispersion =$\frac{(max-min) }{max+min}$ =$\frac{17}{25}$ =0.4857

Variance =(standard deviation )^2

Variance =(3.7972)^2=14.4184

Kurtosis =$\frac{\sum(xi-meanx)^4}{\sum((xi-(meanx)^2)^2}$ =$\frac{7499.353}{577166.8}$

Kurtosis =0.012993

The table below shows the computation of cumulative frequency ,fx,F(x-mean x)^2 and (xi-(mean x)^2)^2