Tool By Zeal Point

Q1. What is the median of the following data ?
65, 67, 32, 16, 64, 27, 37, 16, 43, 85, 77

Solution: Arrange in ascending order: 16, 16, 27, 32, 37, 43, 64, 65, 67, 77, 85

Number of observations = 11

Median = $11+12 = 6th$ observation

Ans: 43

Q2. The mean of a data is 76 and its median is 100. Find the mode using the empirical relation.

Solution: Empirical relation:

$Mode = 3(Median) - 2(Mean)$ $= 3(100)-2(76)$ $= 300 - 152 = 148$

Ans: 148

Q3. The median and mean of a data are 45 and 50 respectively. Find the mode.

$Solution:$

$Mode = 3(Median) - 2(Mean)$ $= 3(45) - 2(50)$ $= 135 - 100 = 35$

Ans: 35

Q4. Find the fourth proportional to 4, 9 and 16.

Let the fourth proportional be $x$ .

$4 : 9 = 16 : x$

$4x = 9 \times 16$

$x = 144/4 = 36$

Ans: 36

Q5. Find the fourth proportional to 3, 5, 8.

If the intended question is 3, 5, 8, then:

$3 : 5 = 8 : x$

$3x = 40$

$x = 40/3 = 13.33$

Q6. Find the mean proportional between 4 and 16.

Mean proportional:

$\sqrt4\times16$ $= \sqrt64 = 8$

Ans: 8