Question

State whether true or false: The mid value of a class interval is 42. If the class-size is 10, the upper and lower limits of the class are 57 and 47 respectively​

Answer 1

Given:

Mid value/class mark of a class interval = 42

Class size = 10

Upper limit = 57

Lower limit = 47

To find:

To state If the mid-value/class mark of the given interval is 42 or not.

Solution:

We've already been given the lower and upper limits of the class interval. To state if 42 is the mid-value of the class interval or not, we'll attempt to find the lower and upper limits of the class interval.

Let us take the upper limit to be y, and the lower limit to be x.

ATQ; Class-size is 10.

∴ y - x = 10 → Eq(1)

(Lower limit (x) is subtracted from the Upper limit (y) since its lower than the upper limit)

ATQ; Classmark/Mid value of the interval is 42.

⇒ (y + x)/2 = 42

⇒ (y + x) = 42 × 2

⇒ y + x = 84 → Eq(2)

Adding equation 1 & 2 we get:

⇒ y - x + y + x = 10 + 84

⇒ 2y = 94

⇒ y = 94/2

⇒ y = 47

⇒ Upper Limit = 47

Substitute the value of 'y' in Eq(2).

⇒ y + x = 84

⇒ 47 + x = 84

⇒ x = 84 - 47

⇒ x = 37

⇒ Lower Limit = 37

Therefore the upper and lower limits are 47 & 37 respectively, but as per the question, the upper and lower limits are 57 & 47.

Hence, the statement is false.