Find the value of P from the following data if its mode is 48.
Class Interval
0 – 10
10 – 20
20 – 30
30 – 40
40 – 50
50 – 60
60 – 70
70 – 80
Frequency
7
14
13
12
P
18
15
8
Answers
Answer:
p = 20
Step-by-step explanation:
Mode of a distribution is given by
Mode = L+ (f−f1)xh/(2f−f1−f2)
Where,
L = Lower class limit of modal group
f = Frequency of the modal group
f1 = Frequency of the preceding class to the modal class
f2 = Frequency of the succeeding class to the modal class
h = Class size
Let us assume p is less than 18
From the given data, 18 is highest frequency, hence modal class = 50 to 60.
L = 50, f = 18 f1 = p, f2 = 15 h = 60 - 50 = 10 and mode = 48
Substituting we get,
48 = 50 + (18 - p)*10/(36 - p - 15)
-2(36 - p - 15) = (18 - p)*10
-42 +2p = 180 - 10p
12p = 222 p = 37/2.
P is a frequency and it should be integer. So above answer is wrong.
So our assumption is not correct.
Hence p > 18
Modal class is 40 to 60.
L = 40, f = p, f1 = 12, f2 = 18, h = 10 and mode = 48.
Substituting in equation we get,
48 = 40 + (p - 12)*10/(2p - 12 - 18)
8(2p - 30) = 10p - 120
6p = 120
P = 20.
Answer:
Refer attachment
