Answer to Question #281820 in Statistics and Probability for Neha

Question

Find the coefficient of quartile deviation from the following:

Class 5 – 10 10 – 15 15 – 20 20 – 25 25 – 30 30 – 35 35 – 40

Frequency 6 8 17 21 15 11 2

9. Find the semi-inter-quartile range for the following data:

Marks 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50

No. of students 22 38 46 35 19

10. Find which of the following industry has less variation if the salaries paid to the employees

are as given below:

Salary (Rs. in

1000’s)

Below

4500

4500 –

4700

4700 –

4900

47900 –

5100

5100 &

above

Industry A 6 13 20 7 6

Industry B 4 9 16 7 0

Answer 1

8.

$n=80$

Q₁ class :

Class with (n/4)th value of the observation in cf (cumulative frequency) column

=(80/4)th value of the observation in cf column

=(20)th value of the observation in cf column

and it lies in the class 15-20.

∴Q₁ class : 15-20

The lower boundary point of 15-20 is 15.

∴L=15

$Q_1=L+\frac{n/4-cf}{f}c=15+\frac{20-14}{17}\cdot5=16.76$

Q₃ class :

Class with (3n/4)th value of the observation in cf (cumulative frequency) column

=(3$\cdot$ 80/4)th value of the observation in cf column

=(60)th value of the observation in cf column

and it lies in the class 25-30.

∴Q₃ class : 25-30

The lower boundary point of 25-30 is 25.

∴L=25

$Q_3=L+\frac{3n/4-cf}{f}c=25+\frac{60-52}{15}\cdot5=27.67$

Coefficient of Quartile deviation:

$\frac{Q_3-Q_1}{Q_3+Q_1}=\frac{27.67-16.76}{27.67+16.76}=0.245$

9.

$n=160$

Q₁ class :

Class with (n/4)th value of the observation in cf (cumulative frequency) column

=(160/4)th value of the observation in cf column

=(40)th value of the observation in cf column

and it lies in the class 10-20.

∴Q₁ class : 10-20

The lower boundary point of 10-20 is 10.

∴L=10

$Q_1=L+\frac{n/4-cf}{f}c=10+\frac{40-22}{38}\cdot10=14.74$

Q₃ class :

Class with (3n/4)th value of the observation in cf (cumulative frequency) column

=(3$\cdot$ 160/4)th value of the observation in cf column

=(120)th value of the observation in cf column

and it lies in the class 25-30.

∴Q₃ class : 30-40

The lower boundary point of 30-40 is 30.

∴L=30

$Q_3=L+\frac{3n/4-cf}{f}c=30+\frac{120-106}{35}\cdot10=34$

semi-inter-quartile range:

$\frac{Q_3-Q_1}{2}=\frac{34-14.74}{2}=9.63$

10.

for A:

Mean:

$\mu=\frac{\sum f_ix_i}{n}=4776.92$

Standard deviation:

$\sigma=\sqrt{\frac{\sum f_ix_i^2-(\sum f_ix_i)^2/n}{n}}=227.54$

Coefficient of Variation:

$k=\sigma/\mu=227.54/4776.92=4.76\%$

for B:

Mean:

$\mu=\frac{\sum f_ix_i}{n}=4744.44$

Standard deviation:

$\sigma=\sqrt{\frac{\sum f_ix_i^2-(\sum f_ix_i)^2/n}{n}}=180.19$

Coefficient of Variation:

$k=\sigma/\mu=180.19/4744.44=3.8\%$

so, industry B has less variation