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Mathematics

The class-mark of a class interval is 42. If the class-size is 10, then the upper and lower limits of the class are

  1. 47 and 37

  2. 47.5 and 37.5

  3. 46.5 and 36.5

  4. 46 and 36

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Answer

Given,

Class size = 10

Class mark = 42

Let upper limit be U and lower limit be L.

As we know,

Class mark = Lower limit + Upper limit2\dfrac{\text{Lower limit + Upper limit}}{2}

⇒42=L + U2⇒L + U=42×2⇒L + U=84….(1)\Rightarrow 42 = \dfrac{\text{L + U}}{2} \\[1em] \Rightarrow \text{L + U} = 42 \times 2 \\[1em] \Rightarrow \text{L + U} = 84 ….(1)

Class size = Upper limit - Lower limit = U - L

⇒ 10 = U - L ….(2)

Adding eq.(1) and (2), we have :

⇒ 84 + 10 = 2U

⇒ 2U = 94

⇒ U = 942\dfrac{94}{2}

⇒ U = 47.

Substituting value of U in eq. (1), we have :

⇒ L + U = 84

⇒ L + 47 = 84

⇒ L = 84 - 47

⇒ L = 37.

Hence option 1 is the correct option.

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