Median

IMPORTANT

Median: Overview

This topic covers concepts, such as Understanding Applications of Measures of Central Tendency, Median as the Middle Most Observation in the Data, Median for Odd Number of Data, Relationship Median of Grouped Data, Median, etc.

Important Questions on Median

HARD
IMPORTANT

Find the median for the given grouped data.

x 50-75 75-100 100-125 125-150 150-175
f 425 625 a 614 320

Where, 

a, is the mode for the continuous data given below.

Class 50-150 150-250 250-350 350-450 450-550
Number of people 50 40 30 100 60

 

MEDIUM
IMPORTANT

Find the median for the given grouped data.

x 15-25 25-35 35-45 45-55 55-65
f 300 a 328 426 320

Where, 

a, is the approximate value of the mode value for the continuous data given below.

Class 50-100 100-150 150-200 200-250 250-300
Number of people 25 50 75 100 125

 

MEDIUM
IMPORTANT

Find the median for the given grouped data.

x 10-30 30-50 50-70 70-90 90-110
f 400 420 a 320 100

Where, 

a, is the approximate value of the mode value for the continuous data given below.

Class 100-200 200-300 300-400 400-500 500-600
Number of people 15 30 45 60 75

 

MEDIUM
IMPORTANT

Find the median for the given grouped data.

x 20-30 30-40 40-50 50-60 60-70
f 10 a+5 2a a+5 10

Where, 

a, is the median for the grouped data given below.

x 11 13 15 17 19
f 15 20 25 20 15

 

MEDIUM
IMPORTANT

Find the median for the given grouped data.

x 3-5 5-7 7-9 9-11 11-13
f 5 7 a+1 2a 4a

Where, 

a, is the median for the grouped data given below.

x 3 5 7 9 11
f 15 25 35 45 55

 

HARD
IMPORTANT

Find the median for the given grouped data.

x 10-15 15-20 20-25 25-30 30-35
f 15 a a+10 25 a+15

Where, 

a, is the median for the grouped data given below.

x 10 15 20 25 30
f 15 30 21 23 19

 

MEDIUM
IMPORTANT

Find the median for the given grouped frequency distribution.

x 12 24 36 42 63
f a 14 a 16 a+6

Where,

a, is the median of the ungrouped data shown below.

5, 7, 6, 8, 10, 8, 11, 12, 17, 15, 19, 22, 21, 25, 23

MEDIUM
IMPORTANT

Find the median for the given grouped frequency distribution.

x 20 21 23 25 27
f 15 17 a 18 21

Where,

a, is the median of the ungrouped data shown below.

8, 7, 9, 12, 10, 13, 14, 17, 15, 18, 22, 20, 24, 29, 27, 26

HARD
IMPORTANT

Find the median for the given grouped frequency distribution.

x 21 23 25 26 29
f 15 14 a 22 33

Where,

a, is the median of the ungrouped data shown below.

6, 8, 7, 9, 15, 13, 11, 19, 17, 25, 30, 26

HARD
IMPORTANT

Find the median for the given grouped frequency distribution.

x 21 23 25 26 29
f 150 147 a 225 325

Where,

a, is the mean for the continuous data given below

Class 50-100 100-150 150-200 200-250
Number of people 100 200 300 400

 

HARD
IMPORTANT

Find the median for the given grouped frequency distribution.

x 11 12 13 14 15
f 410 441 a 440 331

Where,

a, is the mean value for the continuous data given below.

Class 310-390 390-510 510-590 590-710
Number of people 350 250 350 450

 

HARD
IMPORTANT

Find the median for the given grouped frequency distribution.

x 20 40 60 80 100
f 310 330 a 370 400

Where,

a, is the mean for the continuous data given below

Class 510-590 590-710 710-790 790-910
Number of people 250 350 150 250

 

MEDIUM
IMPORTANT

In the following question given below, on solving the given statement, we get quantities I and II, solve both quantities and choose the correct option.

Quantity I: Find the median for the given grouped frequency distribution.

x 2 4 6 8 10
f 31 33 35 37 40

Quantity II: Find the median for the given grouped frequency distribution.

x 3 5 7 9 11
f 41 43 45 47 50

 

HARD
IMPORTANT

In the following question given below, on solving the given statement, we get quantities I and II, solve both quantities and choose the correct option.

Quantity I: Find the median for the given grouped frequency distribution.

x 11 12 13 14 15
f 42 52 57 63 30

Quantity II: Find the median for the given grouped frequency distribution.

x 6 7 13 14 21
f 24 15 27 23 59

 

HARD
IMPORTANT

In the following question given below, on solving the given statement, we get quantities I and II, solve both quantities and choose the correct option.

Quantity I: Find the median for the given grouped frequency distribution.

x 10 20 30 40 50
f 100 150 175 200 225

Quantity II: Find the median for the given grouped frequency distribution.

x 50 40 30 20 10
f 145 130 135 120 110

 

MEDIUM
IMPORTANT

Find the median of the ungrouped data shown below.

8, 9, 13, 10, 15, 19, 17, 20, 22, 21, 25, 23

MEDIUM
IMPORTANT

Find the median of the ungrouped data shown below.

10, 13, 11, 15, 17, 16, 19, 21, 20, 22, 25, 23, 26

HARD
IMPORTANT

 For the following ungrouped data:

15, 18, 17, x, 18, x+1, 21, x+1, 24, 22, 26

If the mean of the above-ungrouped data is 20, then find the median for the ungrouped data.

(Note: x is less than 21 but more than 18)

HARD
IMPORTANT

 For the following ungrouped data:

15, 8, 8, 6, x, x+1, 13, 11, 15, 5

If the mean of the above-ungrouped data is 10, then find the median for the ungrouped data.

(Note: x is less than 11 but more than 8)

HARD
IMPORTANT

For the following ungrouped data:

10, 13, 11, x, 14, x, x+1, 17, 18

If the mean of the above-ungrouped data is 1413, then find the median for the ungrouped data.

(Note: x is less than 17 but greater than 14)