Median for Grouped Data

Q.

Find the median class for the given distribution:
$\begin{array}{cccccc}\text{Weekly Wages (in Rs.)}& 0-100& 100-200& 200-300& 300-400& 400-500\\ \text{No. of Workers}& 40& 39& 34& 30& 45\end{array}$

1. 200-300

2. 300-400

3. 100-200

4. 400-500

Q.

The median for the data is :

$\begin{array}{cccccccc}\text{IQ}& 60-70& 70-80& 80-90& 90-100& 100-110& 110-120& 120-130\\ \text{No. of pupils}& 2& 3& 5& 16& 14& 13& 7\end{array}$

1. 103.26

2. 102.86

3. 98.46

4. 97.47

Q.

The median class for the following 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. 155-160
2. 145-150
3. 150-155
4. 140-145

Q.

The following are the marks obtained in Science by students in class X.
The mean was calculated to be 63.33.
Is this mean an appropriate representation of the average marks obtained?
If no, what would be the most appropriate measure of central tendency for the correct representation of the marks distribution?
What is the value of this measure of central tendency for the given data?

$\begin{array}{cc}\text{Marks}& \text{Frequency}\\ 10-20& 1\\ 20-30& 0\\ 30-40& 0\\ 40-50& 0\\ 50-60& 1\\ 60-70& 5\\ 70-80& 15\\ 80-90& 20\\ 90-100& 3\end{array}$

1. No, median, value of median = 80.12

2. No, mode, value of mode = 85

3. Yes, mean is the best measure of an average

4. Yes, the value of mean represents this data the best

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

Q.

The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality.
Find the median of the data.

$\begin{array}{cc}\text{Monthly consumption (in units)}& \text{Numbers of customers}\\ 65-85& 4\\ 85-105& 5\\ 105-125& 13\\ 125-145& 20\\ 145-165& 14\\ 165-185& 8\\ 185-205& 4\end{array}$

1. 137

2. 140

3. 147

4. 132

Q.

Draw a Ogive for the following distribution which shows the marks of 100 students, then find the median

$$\begin{array}{ccccccccc}\text{Marks}& \text{0-10}& \text{10-20}& \text{20-30}& \text{30-40}& \text{40-50}& \text{50-60}& \text{60-70}& \text{70-80}\\ \text{Number of students}& \text{5}& \text{10}& \text{20}& \text{25}& \text{15}& \text{12}& \text{9}& \text{4}\end{array}$$

1. 8

2. 9

3. 6

4. 7

Q.

Find the median class for the given distribution:
$\begin{array}{cccccc}\text{Weekly Wages (in Rs.)}& 0-100& 100-200& 200-300& 300-400& 400-500\\ \text{No. of Workers}& 40& 39& 34& 30& 45\end{array}$

1. 100-200

2. 400-500

3. 300-400

4. 200-300

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.

$\begin{array}{cc}\text{Length (in mm)}& \text{Number of leaves}\\ 118-126& 3\\ 127-135& 5\\ 136-144& 9\\ 145-153& 12\\ 154-162& 5\\ 163-171& 4\\ 172-180& 2\end{array}$

Find the median length of leaves.

1. 123.45
2. 143.55
3. 146.75
4. 134.75

Q.

100 surnames were randomly picked up from a local telephone directory & the frequency distribution of the number of letters in the English alphabets in the surname was obtained as follows.

$\begin{array}{ccccccc}\text{Number of letters}& 1-4& 4-7& 7-10& 10-13& 13-16& 16-19\\ \text{Number of surnames}& 6& 30& 40& 16& 4& 4\end{array}$
Determine the median number of letters in the surnames.

1. 8.05
2. 9.05
3. 10.05
4. 7.55