Graphical Representation of Statistical Data — Assertion-Reason Type Questions

Assertion (A) : For constructing frequency polygon, class-marks should be calculated.

Reason (R) : To construct a frequency polygon, we take class marks along x-axis and corresponding frequencies along y-axis.

1. Both A and R are true, and R is the correct explanation of A.

2. Both A and R are true, but R is not the correct explanation of A.

3. A is true, but R is false.

4. A is false, but R is true.

Answer

A frequency polygon is drawn by plotting frequencies against class marks (mid-points) of class intervals. So, class-marks must be calculated.

∴ Assertion (A) is true.

To construct a frequency polygon, we mark points taking values of class-marks along x-axis and the values of their corresponding frequencies along y-axis.

∴ Reason (R) is true.

Since the class-marks are required precisely because they are plotted along the x-axis, Reason (R) correctly explains Assertion (A).

Hence, option 1 is the correct option.

Assertion (A) : If the class-mark of a class is 9.5 and the class size is 6, then the class interval is 6 - 12.

Reason (R) : Class mark = $\dfrac{\text{upper limit + lower limit}}{2}$

1. Both A and R are true, and R is the correct explanation of A.

2. Both A and R are true, but R is not the correct explanation of A.

3. A is true, but R is false.

4. A is false, but R is true.

Answer

As we know,

Class mark = $\dfrac{\text{upper limit + lower limit}}{2}$ ...(1)

∴ Reason (R) is true.

Given,

Class mark = 9.5

Class size = 6

Let upper limit be U and lower limit be L.

Susbtituting values in eq.(1), we get:

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

$\Rightarrow 9.5 = \dfrac{\text{L + U}}{2} \\[1em] \Rightarrow \text{L + U} = 9.5 \times 2 \\[1em] \Rightarrow \text{L + U} = 19 ....(2)$

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

⇒ 6 = U - L ....(3)

Adding eq.(2) and (3), we have:

⇒ 19 + 6 = 2U

⇒ 2U = 25

⇒ U = $\dfrac{25}{2}$

⇒ U = 12.5

Substituting value of U in eq.(2), we have:

⇒ L + U = 19

⇒ L + 12.5 = 19

⇒ L = 19 - 12.5

⇒ L = 6.5

∴ Class interval is 6.5 - 12.5

∴ Assertion (A) is false.

Hence, option 4 is the correct option.