Finding Median of Grouped Data When Class Intervals Are Not Given

Q.

Calculate the median from the following data:

Marks	0 – 10	10 – 30	30 – 60	60 – 80	80 – 90
Number of students	5	15	30	8	2

Q. Find the middle term of the A.P. 213, 205, 197, ...., 37.

Q. If the median of the data: 24, 25, 26, x + 2, x + 3, 30, 31, 34 is 27.5, then x =

(a) 27
(b) 25
(c) 28
(d) 30

Q. If the median of the data: 6, 7, x − 2, x, 17, 20, written in ascending order, is 16. Then x =

(a) 15
(b) 16
(c) 17
(d) 18

Q. If 35 is removed from the data: 30, 34, 35, 36, 37, 38, 39, 40, then the median increased by

(a) 2
(b) 1.5
(c) 1
(d) 0.5

Q.

The weekly income of 600 families is tabulated below: Weekly income Number of families (in Rs) 0-1000:250 1000-2000:190 2000-3000:100 3000-4000:40 4000-5000:15 5000-6000: 5 Total 600 Compute the median income.

Q. If a is the missing frequency such that 1 < a < 8, then the median of the given frequency distribution cannot be

Class interval	Frequency
100 - 110	12
110 - 120	6
120 - 130	10
130 - 140	a
140 - 150	8
150 - 160	12

1. 126
2. 128
3. 129
4. 127

Q.

The Life insurance agent found the following data for the distribution of ages of 100 policyholders. Calculate the median age, if policies are given only to the

persons whose age is 18 years onwards but less than 60 years.

Age in years	No. of Policy holders
$\mathrm{Below}20$	$2$
$\mathrm{Below}25$	$6$
$\mathrm{Below}30$	$24$
$\mathrm{Below}35$	$45$
$\mathrm{Below}40$	$78$
$\mathrm{Below}45$	$89$
$\mathrm{Below}50$	$92$
$\mathrm{Below}55$	$98$
$\mathrm{Below}60$	$100$

Q. Question 01.
The median of an ungrouped data and the median calculated when the same data is grouped are always the same. Do you think that this is a correct statement ? Give reason.

Q.

Find the missing frequencies and the median for the following distribution if the mean is 1.46.
No. of accidents: 0 1 2 3 4 5 Total
Total Frequency (No. of days): 46 ? ? 25 10 5 200

Q. The following table shows the ages of persons who visited a museum on a certain day. Find the median age of the persons visiting the museum.

Q. Calculate mean deviation about Median for the following data :

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	6	7	15	16	4	2

Q.

Compute the median from the following data:

Marks Obtained	$0-7$	$7-14$	$14-21$	$21-28$	$28-35$	$35-42$	$42-49$
Number of Students	$3$	$4$	$7$	$11$	$0$	$16$	$9$

Q.

The median of first 8 prime numbers is

(a) 7 (b) 9 (c) 11 (d) 13

Q.

The median of 19 observations is 30.Two more observations are made and the values of these are 8 and 32.Find the median of the 21 observations taken together.

Q. A data has 25 observations arranged in a descending order. Which observation represents the median?
[CBSE 2014]

Q.

If the median of $\frac{x}{5},\frac{x}{4},\frac{x}{2},x,and,\frac{x}{3},wherex>0,is8,$ find the value of x.

Q.

Find the median of: 7, 12, 15, 6, 20, 8, 4 and 10

1. 8

2. 9

3. 10

4. 11

Q.

The median of $\frac{x}{5},\frac{x}{4},\frac{x}{3},\frac{x}{2},x$ $\left(x>0\right)$ is $8$, then the value of $x$ is

1. $24$

2. $32$

3. $8$

4. $16$

5. $40$

Q.

The median of first ten natural numbers is

1. 5

2. 11

3. 6

4. 5.5

Q. Following are the lives in hours of 15 pieces of the components of aircraft engine. Find the median:

715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719

Q.

If the median of the data $4,7,x-1,x-3,16,25$, written in ascending order, is 13 then x is equal to

(a) 13 (b) 14 (c) 15 (d) 16

Q.

Find the median of the following :

$5,7,8,9,11,13,15$

Q.

The lengths 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)	Number or leaves fi
118 − 126	3
127 − 135	5
136 − 144	9
145 − 153	12
154 − 162	5
163 − 171	4
172 − 180	2

Find the median length of the leaves.

(Hint: The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 − 126.5, 126.5 − 135.5… 171.5 − 180.5)

Q.

You ask $100$ randomly chosen dog owners in your town how many dogs they own. The results are shown in the table. There are 500 dog owners in your town.

Estimate the median number of dogs per dog owner in your town. Justify your answer.

Q.

The median class for the given data is

$$\begin{array}{ccccccc}\text{Height (in cm)}& \text{Less than 140}& \text{Less than 145}& \text{Less than 150}& \text{Less than 155}& \text{Less than 160}& \text{Less than 165}\\ \text{No. of girls}& 4& 11& 29& 40& 46& 51\end{array}$$

1. 145 - 150

2. 150 - 155

3. 155 - 160

4. 160 - 165

Q.

The median of ${}^{2n}C_0,{}^{2n}C_1,{}^{2n}C_2,{}^{2n}C_3,.....,{}^{2n}C_n$ (where $n$ is even)

1. ${}^{2n}C_{\frac{n}{2}}$

2. ${}^{2n}C_{\frac{n+1}{2}}$

3. ${}^{2n}C_{\frac{n-1}{2}}$

4. None of these

Q.

A data has 25 observations arranged in a ascending order.Which observation represents the median?

Q. The median of first 10 prime numbers is

(a) 11
(b) 12
(c) 13
(d) 14

Q.

Find the arithmetic mean of the following frequency distribution using the step deviation method.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$9$	$12$	$15$	$10$	$14$