Mathematics

Consider the following class intervals of a grouped data :
Class interval 10-25 25-40 ------- 55-70
Statement 1: Class marks of the 3^rd class intervals is 46.5.
Statement 2: If the class mark of 2^nd interval is 77.5, the interval is 60 - 85.
Which of the following options is correct?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.

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Given,

Class interval	10-25	25-40	-------	55-70

3^rd class interval = 40 - 55

By formula,

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

= $\dfrac{40 + 55}{2}$

= $\dfrac{95}{2}$

= 47.5

So, statement 1 is false.

The class mark of 2^nd interval = 77.5.

Let the interval be x - y.

$\Rightarrow \dfrac{x + y}{2} = 77.5\\[1em] \Rightarrow x + y = 77.5 \times 2\\[1em] \Rightarrow x + y = 155 …………….(1)$

We know that,

The width of the every interval is 15.

⇒ y - x = 15 …………….(2)

Adding equation (1) and (2), we get :

⇒ (x + y) + (y - x) = 155 + 15

⇒ x + y + y - x = 170

⇒ 2y = 170

⇒ y = $\dfrac{170}{2}$

⇒ y = 85.

Substituting the value of y in equation (1), we get :

⇒ x + 85 = 155

⇒ x = 155 - 85

⇒ x = 70.

Thus, interval is 70 - 85.

So, statement 2 is false.

∴ Both the statements are false.

Hence, option 2 is the correct option.

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