Finding Median for Grouped Data When Class Intervals Are Given

Q.

Find the median of the following data:

Class interval	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	Total
Frequency	$8$	$16$	$36$	$34$	$6$	$100$

Q.

The following table gives the marks obtained by 50 students in a class test:

Marks	11−15	16−20	21−25	26−30	31−35	36−40	41−45	46−50
Number of students	2	3	6	7	14	12	4	2

Calculate the mean, median and mode for the above data.

Q. An incomplete distribution is given below :

Variable:	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Frequency:	12	30	−	65	−	25	18

You are given that the median value is 46 and the total number of items is 230.
(i) Using the median formula fill up missing frequencies.
(ii) Calculate the AM of the completed distribution.

Q.

The distribution below gives the weights of 30 students of a class. Find the median weight of the students.

Weight (in kg)	40 − 45	45 − 50	50 − 55	55 − 60	60 − 65	65 − 70	70 − 75
Number of students	2	3	8	6	6	3	2

Q. 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: 20-30 30-40 40-50 50-60 60-70 70-80 80-90

Frequency: p 15 25 20 q 8 10

Q. Find the mean, median and mode of the following data:

Class	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	6	8	10	15	5	4	2

Q. Compute the median for each of the following data:

(i)

Marks	No. of students
Less than 10 Less than 30 Less than 50 Less than 70 Less than 90 Less than 110 Less than 130 Less than 150	0 10 25 43 65 87 96 100

(ii)

Marks	No. of students
More than 150 More than 140 More than 130 More than 120 More than 110 More than 100 More than 90 More than 80	0 12 27 60 105 124 141 150

Q.

The median of the distribution given below is 14.4. Find the values of x and y, if the total frequency is 20.
Class interval: 0-6 6-12 12-18 18-24 24-30
Frequency: 4 x 5 y 1

Q. Find the median of the following data

Class	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
Frequency	5	3	4	3	3	4	7	9	7	8

Q. The length of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:

Length (in mm):	118−126	127−135	136−144	145−153	154−162	163−171	172−180
No. of leaves	3	5	9	12	5	4	2

Find the mean length of leaf.

Q. The annual profits earned by 30 shops of a shopping complex in a locality give rise to the following distribution:

Profit (in lakhs in Rs)	Number of shops (frequency)
More than or equal to 5 More than or equal to 10 More than or equal to 15 More than or equal to 20 More than or equal to 25 More than or equal to 30 More than or equal to 35	30 28 16 14 10 7 3

Draw both ogives for the above data and hence obtain the median.

Q.

If the median of the following data is $32.5,$ find the missing frequencies.
$\begin{array}{ccccccccc}\text{Class Interval}:& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70& \text{Total}\\ \text{Frequency:}& f_1& 5& 9& 12& f_2& 3& 2& 40\end{array}$

Q.

Find the sum of the lower limit of median class and a modal class of the following distribution

$\begin{array}{|cccccc|}\hline \mathrm{Distribution}& 0-5& 5-10& 10-15& 15-20& 20-25\\ \mathrm{Frequency}& 10& 15& 12& 20& 9\\ \hline\end{array}$

Q.

Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.

Age in years	0-10	10-20	20-30	30-40	40-50
No. of persons	5	25	?	18	7

Q.

Find the following table gives the distribution of the life time of 400 neon lamps:

Life time (in hours)	Number of lamps
1500 − 2000	14
2000 − 2500	56
2500 − 3000	60
3000 − 3500	86
3500 − 4000	74
4000 − 4500	62
4500 − 5000	48

Find the median life time of a lamp.

Q. Find the missing frequencies in the following frequency distribution table, if N = 100 and median is 32.

Marks obtained	0−10	10−20	20−30	30−40	40−50	50−60	Total
No. of Students	10	?	25	30	?	10	100

Q. A survey regarding the height (in cm) of 51 girls of class X of a school was conducted and the following data was obtained:

Height in cm	Number of Girls
Less than 140 Less than 145 Less than 150 Less than 155 Less than 160 Less than 165	4 11 29 40 46 51

Find the median height.

Q.

The median of the following data is 16. Find the missing frequencies a and b if the total of frequencies is 70.
$\begin{array}{ccccccccc}\text{Class}& 0-5& 5-10& 10-15& 15-20& 20-25& 25-30& 30-35& 35-40\\ \text{Frequency}& 12& a& 12& 15& b& 6& 6& 4\end{array}$

Q. Find the mean, median and mode of the following data:

Classes:	0−20	20−40	40−60	60−80	80−100	100−120	120−140
Frequency:	6	8	10	12	6	5	3

Q. The following table gives the frequency distribution of married women by age at marriage:

Age (in years)	Frequency	Age (in years)	Frequency
15−19 20−24 25−29 30−34 35−39	53 140 98 32 12	40−44 45−49 50−54 55−59 60 and above	9 5 3 3 2

Calculate the median and interpret the results.

Q.

Find the median from the following data:
$\begin{array}{cc}\text{Marks}& \text{No. of students}\\ \text{Below 10}& 12\\ \text{Below 20}& 32\\ \text{Below 30}& 57\\ \text{Below 40}& 80\\ \text{Below 50}& 92\\ \text{Below 60}& 116\\ \text{Below 70}& 164\\ \text{Below 80}& 200\end{array}$

Q. The following is the cumulative frequency distribution ( of less than type ) of 1000 persons each of age 20 years and above . Determine the mean age .

Age below (in years) : 30 40 50 60 70 80

Number of persons: 100 220 350 750 950 1000

Q.

In a hospital, the ages of diabetic patients were recorded as follows. Find the median age.
$\begin{array}{cccccc}\text{Age (in years)}& 0-15& 15-30& 30-45& 45-60& 60-75\\ \text{Numbers of patients}& 5& 20& 40& 50& 25\end{array}$

Q.

An incomplete distribution is given as follows:
Variable: 0 -10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70
Frequency: 10 20 ? 40 ? 25 15
You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.

Q.

A survey regarding the height (in cm) of 51 girls of class X of a school was conducted
and the following data was obtained:
$$\begin{array}{cc}& \\ \text{Height in cm}& \text{Number of Girls}\\ \text{Less than 140}& 4\\ \text{Less than 145}& 11\\ \text{Less than 150}& 29\\ \text{Less than 155}& 40\\ \text{Less than 160}& 46\\ \text{Less than 165}& 51\end{array}$$
Find the median height.

Q.

The following table shows the daily wages of workers in a factory:
$\begin{array}{cccccc}\text{Daily eages (in Rs)}& 0-100& 100-200& 200-300& 300-400& 400-500\\ \text{Number of workers}& 40& 32& 48& 22& 8\end{array}$
Find the median daily wage income of the workers.

Q. 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
(a) 17 (b) 17.5 (c) 18 (d) 18.5

Q.

Find the median from the following data: $\begin{array}{cccccccccc}\text{Class}& 1-5& 6-10& 11-15& 16-20& 21-25& 26-30& 31-35& 36-40& 41-45\\ \text{Frequency}& 7& 10& 16& 32& 24& 16& 11& 5& 2\end{array}$

Q.

In the following data the median of the runs scored by $60$ top batsmen of the world in one-day international cricket matches is $5000$. Find the missing frequencies $x$ and $y$.

Runs scored	2500-3500	3500-4500	4500-5500	5500-6500	6500-7500	7500-8500
Number of batsman	5	x	y	12	6	2

Q. Following is the distribution of I.Q. of 100 students. Find the median I.Q.

I.Q.:	55−64	65−74	75−84	85−94	95−104	105−114	115−124	125−134	135-144
No. of students:	1	2	9	22	33	22	8	2	1