Question

Match List-I with List-II. A data contains the following eight values:
\[ 4,3,0,5,2,9,4,5 \]

List-I		List-II
(A)	Range of data minus \(4\)	(II)	\(5\)
(B)	Mean Deviation	(IV)	\(1.75\)
(C)	Variance	(III)	\(6\)
(D)	Median	(I)	\(4\)

• A. A-III, B-I, C-IV, D-II
• B. A-III, B-I, C-IV, D-III
• C. A-III, B-IV, C-II, D-I
• D. A-II, B-IV, C-III, D-I

Hint:

For variance, use \(\sigma^2=\frac{\sum x^2}{n}-\bar{x}^2\). For median, first arrange the data.

Answer 1

The Correct Option is D

Concept:
We calculate range, mean deviation, variance and median from the given data.

Step 1: Range of data. \[ \text{Largest value}=9,\quad \text{Smallest value}=0 \] \[ \text{Range}=9-0=9 \] \[ \text{Range}-4=9-4=5 \] So: \[ A\rightarrow II \]

Step 2: Median.
Arrange data: \[ 0,2,3,4,4,5,5,9 \] Median: \[ \frac{4+4}{2}=4 \] So: \[ D\rightarrow I \]

Step 3: Mean and variance.
Mean: \[ \bar{x}=\frac{4+3+0+5+2+9+4+5}{8} \] \[ \bar{x}=\frac{32}{8}=4 \] \[ \sum x^2=16+9+0+25+4+81+16+25=176 \] \[ \sigma^2=\frac{176}{8}-4^2=22-16=6 \] So: \[ C\rightarrow III \]

Step 4: Mean deviation. \[ \frac{|4-4|+|3-4|+|0-4|+|5-4|+|2-4|+|9-4|+|4-4|+|5-4|}{8} \] \[ =\frac{0+1+4+1+2+5+0+1}{8} \] \[ =\frac{14}{8}=1.75 \] So: \[ B\rightarrow IV \] \[ \therefore \text{Correct Answer is (D)} \]