Question

The mean of the mode, median and range of the following marks obtained by 20 students 4, 6, 5, 9, 3, 2, 7, 7, 6, 5, 4, 9, 10, 10, 3, 4, 7, 6, 9, 9 is approximately

• A. 5.5
• B. 7.67
• C. 6.66
• D. 8

Answer 1

The correct option is B 7.67

The 20 observations are arranged in ascending order as:
2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 9, 9, 9, 9, 10, 10
Range of data = Maximum value – Minimum value
= 10 – 2
= 8
Mode of data = Maximum frequency = 9
Median of 20 observations = $\frac{(\frac{n}{2}{)}^{th}\text{term}+(\frac{n}{2}+1{)}^{th}\text{term}}{2}$ ($\therefore 20$ is even)
$=\frac{{10}^{th}\text{term}+{11}^{th}\text{term}}{2}$
$=\frac{6+6}{2}$
$=\frac{12}{2}$
= 6
Mean of mode, median and range $=\frac{8+9+6}{3}$
$=7.67$
Hence, the correct answer is option (b).