Question

In a frequency distribution, the mid-value of a class is 10 and the width of the class is 6. The lower limit of the class is ______.

Options

• 6

• 7

• 8

• 12

Answer 1

In a frequency distribution, the mid-value of a class is 10 and the width of the class is 6. The lower limit of the class is 7.

Explanation:

Given: Mid-value = 10

Range = 6

Let the upper class and lower class of the interval be x and y, respectively.

Now, Mid-value = `("Upper class" + "Lower class")/2`

`10 = (x + y)/2`

x + y = 20  ...(I)

As, Range = Maximum value of data set – Minimum value of data set

6 = x – y

x – y = 6  ...(II)

Adding equation (I) and (II), we get

x + y + (x – y) = 20 + 6

2x = 26

`x = 26/2`

x = 13

Putting the value of x in equation (I), we get

13 + y = 20

y = 20 – 13

y = 7

Hence, the lower limit of the class is 7.