Calculate the value of variance if median =23
mode = 29 and coefficient of variation is 50%.
10​

1 thought on “Calculate the value of variance if median =23<br />mode = 29 and coefficient of variation is 50%.<br />10​”

1. SOLUTION

   GIVEN

   Median = 23 , mode = 29 and coefficient of variation is 50%

   TO DETERMINE

   The value of variance

   EVALUATION

   Here it is given that median = 23 , mode = 29

   We know that

   Mode + 2 × Mean = 3 × Median

   ⇒ 29 + 2 × Mean = 3 × 23

   ⇒ 29 + 2 × Mean = 69

   ⇒ 2 × Mean = 40

   ⇒ Mean = 20

   Now

   [tex]\displaystyle\sf{ Coefficient \: of \: Variation = \frac{Standard \: Deviation }{Mean} \times 100 }[/tex]

   [tex]\displaystyle\sf{ \implies \: \frac{Standard \: Deviation }{20} \times 100 = 50}[/tex]

   [tex]\displaystyle\sf{ \implies \: Standard \: Deviation = 10}[/tex]

   Now value of variance

   [tex]\displaystyle\sf{ = {( Standard \: Deviation) }^{2} }[/tex]

   [tex]\displaystyle\sf{ = {10}^{2} }[/tex]

   [tex] = 100[/tex]

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