Median

Q. Calculate the median from the following data:

Marks below:	10	20	30	40	50	60	70	80
No. of students:	15	35	60	84	96	127	198	250

Q. Find the median for the given data by drawing a 'less than ogive': [6 MARKS]
$\begin{array}{cccccc}Classinterval& 0-10& 10-20& 20-30& 30-40& 40-50\\ Frequency& 4& 9& 15& 14& 8\end{array}$

Q.

Find the median of the first ten prime numbers?

Q.

From the following frequency distribution, find the median class:

$\begin{array}{ccccc}\text{Cost of living index}& 1400-1550& 1550-1700& 1700-1850& 1850-2000\\ \text{Number of weeks}& 8& 15& 21& 8\end{array}$

Q.

If $\frac{n}{2}$ =any of the given $Cf$ then what is the median class

Q.

The table below gives the percentage distribution of female teachers in the primary school of rural areas of various States and Union Territories (UT) of India. Find the median, mean and mode of the data.

% of female teachers	$15-25$	$25-35$	$35-45$	$45-55$	$55-65$	$65-75$	$75-85$
No. of states/UT	$6$	$11$	$7$	$4$	$4$	$2$	$1$

Q.

Find the median of the following data distribution.
$\begin{array}{ccccccccc}\text{Marks obtained}& 20& 29& 28& 33& 42& 38& 43& 25\\ \text{Number of students}& 6& 28& 24& 15& 2& 4& 1& 20\end{array}$

1. 28.5

2. 29

3. 30

4. 40

Q.

Class Interval	$0-100$	$100-200$	$200-300$	$300-400$	$400-500$	$500-600$	$600-700$	$700-800$	$800-900$	$800-900$
Frequency	$2$	$5$	$x$	$12$	$17$	$20$	$y$	$9$	$7$	$4$

The median of the following data is $525$.

Find the value of $x$ and $y$, if the total frequency is $100$.

Q.

100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabet in the surnames was obtained as follows:
$\begin{array}{ccccccc}Numberofletters& 1-4& 4-7& 7-10& 10-13& 13-16& 16-19\\ Numberofsurnames& 6& 30& 40& 16& 4& 4\end{array}$

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, find the modal size of the surnames.

Q. Calculate the median from the following data:

Rent (in Rs.):	15−25	25−35	35−45	45−55	55−65	65−75	75−85	85−95
No. of Houses:	8	10	15	25	40	20	15	7

Q.

If $a_1,a_2,...a_{50}$are in GP, then$(a_1-a_3+a_5-...+a_{49})/(a_2-a_4+a_6-...+a_{50})$is equal to

1. $a_2/a_5$

2. $a_4/a_6$

3. $a_1/a_2$

4. $a_6/a_1$

Q.

If y is the mean proportional between x and z prove that

xyz(x+y+z)^3=(xy+yz+zx)^3

Q.

From the following data, find the median age of $100$ residents of a colony who took part in Swachh Bharat Abhiyan:

$\begin{array}{cc}\text{Age(in yrs.) More}& \text{No. of residents}\\ \text{than or equal to}& \\ 0& 50\\ 10& 46\\ 20& 40\\ 30& 20\\ 40& 10\\ 50& 3\end{array}$

Q.

The mean proportional between two numbers is 28 and their third proportional to them is 224. The two numbers are

Q.

The lengths of 40 leaves in a plant are measured correctly to the nearest millimeter, and the data obtained is represented as in the following table: Find the median length of leaves.

Length in mm	Number of leaves
$118-126$	$3$
$127-135$	$5$
$136-144$	$9$
$145-153$	12
$154-162$	$5$
$163-171$	$4$
$172-180$	$2$

Q. The following is the distribution of height of students of a certain class in a certain city:

Height (in cms):	160−162	163−165	166−168	169−171	172−174
No. of students:	15	118	142	127	18

Find the median height.

Q.

Find two no. such that the mean propoortional between them is 28 and the third proportional to them is 224.

Q. Formula for calculating median of grouped data is:
$l+\left[\frac{\frac{n}{2}-cf}{f}\right]\times h$

1. True
2. False

Q.

Find the median of the given data:-

$5.6,7.2,1.8,4.3,9.1,2.6,3.4$

Q.

Using a graph paper, draw an ogive for the following distribution which shows the marks obtained in the General Knowledge paper by 100

$\begin{array}{ccccccccc}Marks& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70& 70-80\\ NO.ofStudent& 5& 10& 20& 25& 15& 12& 9& 4\end{array}$

Use the ogive to estimate:

(i) the median.
(ii) the number of students who score marks above 65 .

1. 38, 8

2. 36, 8

3. 8, 36

4. 36, 10

Q.

The correct formula for finding the median of a grouped data is

1. 

2. 

3. 

4. 

Q.

Find the median class for the below distribution.
$\begin{array}{cc}\text{Class}& \text{Cumulative frequency}\\ 10-20& 3\\ 20-30& 17\\ 30-40& 24\\ 40-50& 33\\ 50-60& 51\end{array}$

1. 20 - 30
2. 30 - 40
3. 40 - 50
4. 50 - 60

Q. In a hospital, the ages of diabetic patients were recorded as follows. Find the median age. [CBSE 2014]

Age (in years)	0−15	15−30	30−45	45−60	60−75
Number of patients	5	20	40	50	25

Q.

A survey was conducted on 20 families in a locality by a group of students .What will be the mode of the data?

$$\begin{array}{cccccc}Ageoffamilymember& 0-20& 20-40& 40-60& 60-80& 80-100\\ Numberofstudents& 7& 8& 2& 2& 1\end{array}$$

1. 21.85

2. 22.85

3. 23.87

4. 24.87

Q.

If A.M of two terms is $9$ and H.M is $36$, then G.M will be

1. $18$

2. $12$

3. $16$

4. None of these

Q.

Question 7
The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
$\begin{array}{cccccccc}Weight\left(inkg\right)& 40-45& 45-50& 50-55& 55-60& 60-65& 65-70& 70-75\\ Numberofstudents& 2& 3& 8& 6& 6& 3& 2\end{array}$

Q.

Find the Median for the given data by drawing a 'less than ogive' :

$\begin{array}{cccccc}\text{Class Interval}& 0-10& 10-20& 20-30& 30-40& 40-50\\ \text{Frequency}& 5& 10& 14& 16& 8\end{array}$

1. 31

2. 35

3. 28

4. 29

Q.

Question 80(ii)

In Delhi University, in the year 2009-10, 49000 seats were available for' admission to various courses at graduation level. Out of these 28200 seats were for the students of General Category while 7400 seats were reserved for SC and 3700 seats for ST. Find the percentage of seats' available for students of SC Category and ST Category taken together.

Q.

1. Median Mark = 56.5, Passing marks: 39, % students got distinction = 20%

2. Median Mark = 56.5, Passing marks: 39, % students got distinction = 60%

3. Median Mark = 56.5, Passing marks: 30, % students got distinction = 20%

4. Median Mark = 50.5, Passing marks: 39, % students got distinction = 20%

5. Median Mark = 50.5, Passing marks: 30, % students got distinction = 20%

6. Median Mark = 50.5, Passing marks: 39, % students got distinction = 10%

Q.

Question 2
During the medical check-up of 35 students of a class, their weights were recorded as follows:
$\begin{array}{cc}Weight\left(inkg\right)& Numberofstudents\\ Lessthan38& 0\\ Lessthan40& 3\\ Lessthan42& 5\\ Lessthan44& 9\\ Lessthan46& 14\\ Lessthan48& 28\\ Lessthan50& 32\\ Lessthan52& 35\end{array}$

Draw a less than type ogive for the given data. Hence, obtain the median weight from the graph verify the result by using the formula.