Question

43. If the mode of the following frequency
distribution is 31, then find the value of p.
Class 5-15 15-25 25-35 35-45 45-55
Frequency 3 p 15 11 6
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Answer 1

Answer:

Hope it helps

Step-by-step explanation:

You have to learn every formula carefully

Answer 2

Given,

Class interval        Frequency

5-15                          3

15-25                       p

25-35                      15

35-45                      11

45-55                      6

Mode of the observation = 31

To find,

We have to find the value of p.

Solution,

If the mode of the following frequency distribution is 31, then find the value of p is 9.

We can simply find the value of p by using the formula of mode,

  Mode = L1 +( f₁ - f₀/2f₁-f₀-f₂) h

where L1 = the lower limit of the modal class

            f₀= frequency preceding the modal class frequency.

            f₁ =   frequency of the modal class

            f₂ = frequency succeeding the modal class frequency

            h = height of the class interval

Class interval        Frequency

5-15                          3

15-25                       p⇒f0

 L1⇒25-35            15⇒ f1    

35-45                      11⇒f2

45-55                      6

h = 10

Substituting the values in the formula of finding mode, we get

Mode = 25 + (15-p)/(30-p-11)10

     31 = 25 + (15-p)/(30-p-11)10

31-25 = (15-p)/(30-p-11)10

      6 = (15-p)10 / (19-p)

114 - 6p = 150-10p

10p -6p = 150-114

        4p = 36

         p = 9

Hence, if the mode of the following frequency distribution is 31, then find the value of p is 9.