Determine (a) Q1’ (b) Q3’ (c) D5’ (d) P80 from the following distribution:
Class 10-15 15-20 20-25 25-30 30-35 35-40
Frequency 20 15 31 22 10 2
Answers
Step-by-step explanation:
We know,
Mode=l+
2f−f
1
−f
2
f−f
1
×h
l= lower limit of the modal class
h= size of the class intervals
f= frequency of the modal class
f
1
= frequency of the class preceding the modal class
f
2
= frequency of the class succeed in the modal class.
(i) Here, the maximum frequency is 28 then the corresponding class 40−52 is modal class.
⇒ l=40,h=50−40=10,f=28,f
1
=12,f
2
=20
⇒ Mode=l+
2f−f
1
−f
2
f−f
1
×h
⇒ Mode=40+
2×28−12−20
28−12
×10
⇒ Mode=40+
24
160
⇒ Mode=40+6.67=46.67
(ii) Here, the maximum frequency is 75, then the corresponding class 20−25 is the modal class.
⇒ l=20,h=25−20=5,f=75,f
1
=45,f
2
=35
⇒ Mode=l+
2f−f
1
−f
2
f−f
1
×h
⇒ Mode=20+
2×75−45−35
75−45
×5
⇒ Mode=20+
70
150
⇒ Mode=20+2.14=22.14
(iii) Here, the maximum frequency is 50 then the corresponding class 35−40 is the modal class.
⇒ l=35,h=40−35=5,f=50,f
1
=34,f
2
=42
⇒ Mode=l+
2f−f
1
−f
2
f−f
1
×h
⇒ Mode=35+
2×50−34−42
50−34
×5
⇒ Mode=35+
24
80
⇒ Mode=35+3.33=38.33