Gujarat Board Statistics Class 11 GSEB Solutions Chapter 4 Measures of Dispersion Ex 4.2 Textbook Exercise Questions and Answers.
Gujarat Board Textbook Solutions Class 11 Statistics Chapter 4 Measures of Dispersion Ex 4.2
Question 1.
A shooter missed his target in the last 10 trials by the following distance (mm) during the practice session:
20, 32, 24, 41, 18, 27, 15, 36, 35, 25
Find the quartile deviation and coefficient of quartile deviation of such distance missed by the shooter.
Answer:
Writing the measures of mistargets in ascending order :
15, 18, 20, 24, 25, 27, 32, 35, 36, 41
Here, n = 10
First Quartile :
Q1 = Value of
= Value of
= Value of 2nd observation +0.75 (Value of 3rd observation – Value of 2nd observation)
= 18 + 0.75 (20 – 18)
= 18 + 0.75 (2)
= 18 + 1.50 = 19.50 mm
Third Quartile :
Q3 = Value of 3
= Value of 3 (2.75) = 8.25th observation
= Value of 8th observation + 0.25 (Value of 9th observation – Value of 8th observation)
= 35 + 0.25 (36-35)
= 35 + 0.25 = 35.25 mm
Quartile deviation of measures of mistargets :
Qd =
Putting Q3 = 35.25; Q1 = 19.50, we get
Qd =
Coefficient of quartile deviation =
=
=
= 0.29
Question 2.
Find the quartile deviation and coefficient of quartile deviation of the marks from the following frequency distribution of marks of 43 students of a school;
Answer:
First Quartile :
Q1 = Value of
= Value of
Referring to column cf,
Q1 = 20 marks
Third Quartile :
Q3 = Value of
= Value of 3(11)
= 33 rd observation Referring to column cf,
Q3 = 40 marks
Quartile deviation of marks:
Question 3.
The distribution of amount paid by 200 customers coming for snacks at a restaurant on a particular day is given below:
Find the quartile deviation and coefficient of quartile deviation of the amount paid by customers on the day.
Answer:
Amount paid ₹ | No. of customers f | Cumulative frequency cf |
0-50 | 25 | 25 |
50- 100 | 40 | 65 |
100-150 | 80 | 145 |
150-200 | 30 | 175 |
200 – 250 | 25 | 200 |
Total | n = 200 | – |
First Quartile:
Q1 Class = Class that Includes
= Class that includes
Referring to column cf
Q1 class = 50 – 100
Now, Q1 = L +
Putting L = 50:
Third Quartile:
Q3 Class = Class that Includes 3
= Class that Includes 3 (50)th = 150th observation
Referring to column cf. Q3 class = 150 – 200
Now. Q3 = L +
Putting L = 150: 3