Find the value of X if mode is 25:
Class
0-10
10-20
20-30
30-40
40-50
50-60
60-70
Fre

1 thought on “Find the value of X if mode is 25:<br />Class<br />0-10<br />10-20<br />20-30<br />30-40<br />40-50<br />50-60<br />60-70<br />Fre”

1. Question:-

   Find the value of x if mode of the given data is 25.

   • DATA:-

   [tex]\boxed{\begin{array}{c|c} \bf{Class} & \sf{Frequency} \\ \cline{1-2} \sf{0-10} & \sf{14} \\ \sf{10 – 20} & \sf{22} \\ \sf{20-30} & \sf{27} \\ \sf{30-40} & \sf{x} \\ \sf{40-50} & \sf{23} \\ \sf{50-60} & \sf{20} \\ \sf{60-70} & \sf{15} \end{array}}[/tex]

   To Find:-

   • The value of x.

   Solution:-

   We have:-

   • Mode = 25

   As we are given in the question that mode of the given data is 25, which lies in the class (20 – 30). Therefore here, the modal class is (20 – 30).

   Now,

   We already know:-

   • [tex]\dag\boxed{\orange{\underline{\red{\tt{Mode = \bigg(l + \dfrac{f_1 – f_0}{2f_1 – f_0 – f_2} \times h \bigg)}}}}}[/tex]

   Where:–

   • l = lower limit of the modal class
   • h = height of the class
   • f₁ = Frequency of the modal class
   • f₂ = Frequency of the succeeding class of the modal class
   • f₀ = Frequency of the preceeding class of the modal class

   From frequency table we already have:–

   • l = 20
   • h = 30 – 20 = 10
   • f₀ = 22
   • f₁ = 27
   • f₂ = x

   Let’s put all the values in the formula:–

   [tex] = \tt{25 = 20 + \dfrac{27 – 22}{2\times 27 – 22 – x} \times 10}[/tex]

   [tex] = \tt{25 – 20 = \dfrac{5}{54 – 22 – x} \times 10}[/tex]

   [tex] = \tt{\dfrac{5}{10} = \dfrac{5}{32 – x}}[/tex]

   [tex] = \tt{5(32 – x) = 10 \times 5}[/tex]

   [tex] = \tt{32 – x = \dfrac{50}{5}}[/tex]

   [tex] = \tt{32 – x = 10}[/tex]

   [tex] = \tt{-x = 10 – 32}[/tex]

   [tex] = \tt{-x = -22}[/tex]

   [tex] = \tt{x = 22}[/tex]

   ∴ The value of x is 22.

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   Verification!!!

   Lets verify our answer by putting all the values in the formula:-

   [tex] = \tt{Mode = 20 + \dfrac{27 – 22}{27 \times 2 – 22 – 22} \times 10}[/tex]

   [tex] = \tt{Mode = 20 + \dfrac{5}{54 – 44} \times 10}[/tex]

   [tex] = \tt{Mode = 20 + \dfrac{5}{10} \times 10}[/tex]

   [tex] = \tt{Mode = 20 + 5}[/tex]

   [tex] = \tt{Mode = 25}[/tex]

   We got Mode = 25.

   Hence, the answer we got is correct [Verified]

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