Question

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

Answer 1

Holaaa Mate

Answer:

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 2

Answer:

p=20

Step-by-step explanation:

Given in the image

Hope this helps you

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