Median of Grouped Data

Author:Neha Tyagi & Amit Rastogi
10th CBSE
IMPORTANT

Median of Grouped Data: Overview

This topic talks about median, the middle value of any distribution of data given. Here, we will find the median for discrete and grouped data with the help of solved examples.

Important Questions on Median of Grouped Data

MEDIUM
IMPORTANT

50 students enter for a school javelin throw competition. The distance (in metre) thrown are recorded below

Distance (in m) 0-20 20-40 40-60 60-80 80-100
Number of students 6 11 17 12 4

Are the median distance calculated in (ii) by drawing ogive and (iii) by cumulative frequency same?

MEDIUM
IMPORTANT

50 students enter for a school javelin throw competition. The distance (in metre) thrown are recorded below

Distance (in m) 0-20 20-40 40-60 60-80 80-100
Number of students 6 11 17 12 4

Calculate the median distance by using the formula for median.

MEDIUM
IMPORTANT

The table below shows the salaries of 280 persons.

Salary (inthousand) Number of persons
5-10 49
10-15 133
15-20 63
20-25 15
25-30 6
30-35 7
40-45 2
45-50 1

Calculate the median and mode of the data.

MEDIUM
IMPORTANT

Draw the less than type and more than type ogives for the data and use them to find the median weight.

The weights of tea in 70 packets shown in the following table

Weight (in g) Number of packets
200-201 13
201-202 27
202-203 18
203-204 10
204-205 1
205-206 1

 

MEDIUM
IMPORTANT

Size of agriculture holdings in a survey of 200 families is given in the following table.

Size of Agricultural Holdings (in hec) Number of families
0-5 10
5-10 15
10-15 30
15-20 80
20-25 40
25-30 20
30-35 5

Compute median and mode size of the holdings.

MEDIUM
IMPORTANT

Draw the less than type ogive for this data and use it to find the median weight.

The weights of tea in 70 packets:

Weight (in g) Number of packets
200-201 13
201-202 27
202-203 18
203-204 10
204-205 1
205-206 1

 

MEDIUM
IMPORTANT

The median of the following data is 50. Find the values of p and q, if the sum of all the frequencies is 90.

Marks Frequency
20-30 p
30-40 15
40-50 25
50-60 20
60-70 q
70-80 8
80-90 10

 

HARD
IMPORTANT

The maximum bowling speeds, in km per hour, of 33 players at a cricket coaching centre are given as follows.

Speed (in km/h) 85-100 100-115 115-130 130-145
Number of players 11 9 8 5

Calculate the median bowling speed.

EASY
IMPORTANT

Will the median class and modal class of grouped data always be different? Justify your answer.

MEDIUM
IMPORTANT

Consider the following frequency distribution

Class 0-5 6-11 12-17 18-23 24-29
Frequency 13 10 15 8 11

The upper limit of the median class is

 

EASY
IMPORTANT

The sum of lower limits of the median class and modal class is

Class 0-5 5-10 10-15 15-20 20-25
Frequency 10 15 12 20 9