Median for Grouped Data

Q.

The median of the following data is 525. Find the values of x and y, if the total frequency is 100.

$\begin{array}{cc}ClassInterval& Frequency\\ 0-100& 2\\ 100-200& 5\\ 200-300& x\\ 300-400& 12\\ 400-500& 17\\ 500-600& 20\\ 600-700& y\\ 700-800& 9\\ 800-900& 7\\ 900-1000& 4\end{array}$ [4 MARKS]

Q.

Question 2
If the median of the distribution given below is 28.5, find the values of x and y.

$\begin{array}{cc}Classinterval& Frequency\\ 0-10& 5\\ 10-20& x\\ 20-30& 20\\ 30-40& 15\\ 40-50& y\\ 50-60& 5\\ Total& 60\end{array}$

Q. If the median of the following frequency distribution is 46, find the missing frequencies. Variable frequency 10-20. 12 20-30. 30 30-40. ? 40-50. 65 50-60. ? 60-70. 25 70-80. 18 Total. 229

Q. Find mean, median and mode
more than - 150 140. 130. 120. 110. 100. 90. 80
Frequency - 0. 12. 27. 60. 105. 124. 141 150

Q. The times (in seconds) taken by 150 athletes to run a 110 m hurdle race are tabulated below

$\begin{array}{ccccccc}\text{Class}& 13.8-14& 14-14.2& 14.2-14.4& 14.4-14.6& 14.6-14.8& 14.8-15\\ \text{Frequency}& 2& 4& 5& 71& 48& 20\end{array}$

The number of athletes who completed the race in less than 14.6 s is ___ .

1. 11
2. 71
3. 82
4. 130

Q.

The median is always one of the numbers in a data. (True or False)

1. True
2. False

Q. Calculate the median for the following distribution.

$\begin{array}{cc}Marksobtained& Numberofstudents\\ Below10& 6\\ Below20& 15\\ Below30& 29\\ Below40& 41\\ Below50& 60\\ Below60& 70\end{array}$

Q.

The monthly income of a group of 320 employees in a company is given below:

Monthly income	6000-7000	7000-8000	8000-9000	9000-10000	10000-11000	11000-12000	12000-13000
No of employees	20	45	65	95	60	30	5

Calculate:

(i) Median wage

(ii) Number of employees whose income is below Rs. 8500

(iii) Number of senior employees in the company

(iv) Upper quartile

[4 MARKS]

Q.

In the given frequency distribution where the marks are ordered, which 2 observations (students) are the median observations?

$$\begin{array}{cc}Marksobtained& Numberofstudents\left(Frequency\right)\\ 20& 6\\ 25& 20\\ 28& 24\\ 29& 28\\ 33& 15\\ 38& 4\\ 42& 2\\ 43& 1\end{array}$$

1. Cannot be determined

2. 50^th term and 49^th term

3. 61^st term and 49^th term

4. 50^th term and 51^st term

Q.

Find the median of the given data.

$\begin{array}{cccccc}\text{Wages (in Rs.)}& 200-300& 300-400& 400-500& 500-600& 600-700\\ \text{No. of Labourers}& 3& 5& 20& 10& 6\end{array}$

1. 420
2. 400
3. 470
4. 300

Q. The following numbers are arranged in descending order of their values:

68, 60, 52, x-3, x-8, x-11, 30, 25, 22, 20

If their median is 39, find the value of x.

1. 38.5
2. 48.5
3. 60
4. 75.5

Q. $$\begin{array}{cccccc}\text{Marks}& \text{Below 10}& \text{Below 20}& \text{Below 30}& \text{Below 40}& \text{Below 50}\\ \text{No. of students}& 5& 10& 23& 31& 40\end{array}$$
The median for the data given above is ____.

1. 26.79
2. 27.69
3. 26.69
4. 29.67

Q. Question 11
Size of agricultural holdings in a survey of 200 families is given in the following table
$\begin{array}{cc}Sizeofagriculturalholdings\left(inhec\right)& Numberoffamilies\\ 0-5& 10\\ 5-10& 15\\ 10-15& 30\\ 15-20& 80\\ 20-25& 40\\ 25-30& 20\\ 30-35& 5\end{array}$
Compute median and size of the holdings.

Q.

The median of the data: $3,4,5,6,7,3.4$. is

1. (a) 5

2. (b) 3

3. (c) 4

4. (d) 6

Q.

How many students scored more than or equal to 30 out of 50 marks in a class.
$\begin{array}{cc}Marks& Numberofstudents\\ 0-10& 2\\ 10-20& 12\\ 20-30& 21\\ 30-40& 8\\ 40-50& 5\end{array}$

1. 13
2. 10
3. 8
4. 2

Q.

The distribution given below shows the marks obtained by 25 students in an aptitude test. Find the mean, median & mode of the following data.

1. 6.24, 7, 6

2. 6.24, 8, 5

3. 6.24, 7, 10

4. 6.84, 8, 5

5. 6.84, 7, 10

6. 6.84, 7, 6

Q.

Frequency table of the marks of 50 students as given below:

Given that the median marks are 28.5, the missing frequencies will be

1. f₁ = 5, f₂ = 7

2. f₁ = 8, f₂ = 7

3. f₁ = 7, f₂ = 5

4. f₁ = 7, f₂ = 9

Q. Find the values of p, q, r and s in the given cumulative frequency distribution.

$\begin{array}{ccc}x& \text{frequency}& \text{Cumulative frequency}\\ 10& 3& p\\ 15& 10& q\\ 20& 25& r\\ 25& 7& s\\ 30& 5& 50\end{array}$

1. p = 3, q = 13, r = 28, s = 35
2. p = 3, q = 13, r = 35, s = 42
3. p = 0, q = 10, r = 35, s = 42
4. p = 3, q = 13, r = 38, s = 45

Q. Following table shows marks (out of 100) of students in a class test:
$\begin{array}{cc}\text{Marks}& \text{No. of students}\\ \text{More than or equal to 0}& 80\\ \text{More than or equal to 10}& 77\\ \text{More than or equal to 20}& 72\\ \text{More than or equal to 30}& 65\\ \text{More than or equal to 40}& 55\\ \text{More than or equal to 50}& 43\\ \text{More than or equal to 60}& 28\\ \text{More than or equal to 70}& 16\\ \text{More than or equal to 80}& 10\\ \text{More than or equal to 90}& 8\\ \text{More than or equal to 100}& 0\end{array}$
Draw a 'more than type' ogive. From the curve, find the median. Also, check the value of the median by actual calculation.

Q.

Find the median class of the following distribution:

1. 300-400

2. 400-500

3. 200-300

4. 500-600

Q.

The mean and the median of a distribution are 45.9 and 46 respectively. The mode will be

1. 48

2. 45

3. 47

4. 46.2

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.

From the following cumulative frequency table, estimate:

(i) The median

(ii) The semi-interquartile range.

1. Median = Rs 50, Semi – interquartile range = 15

2. Median = Rs 62, Semi – interquartile range = 20

3. Median = Rs 50, Semi – interquartile range = 20

4. Median = Rs 62, Semi – interquartile range = 15

Q.

What are more appropriate measures of center and spread for a data set? Select two choices: one for the center and one for the spread.

1. Better measure of center: mean

2. Better measure of spread: interquartile (IQR)

3. A better measure of center: median

4. Better measure of spread: standard deviation

Q. If the median of the following frequency distribution is $28.5$, then find the missing frequencies.

Class interval:	0-10	10-20	20-30	30-40	40-50	50-60	Total
Frequency:	$5$	$f_1$	$20$	$15$	$f_2$	$5$	$60$

Q. The times (in seconds) taken by 150 athletes to run a 110 m hurdle race are tabulated below

$\begin{array}{ccccccc}\text{Class}& 13.8-14& 14-14.2& 14.2-14.4& 14.4-14.6& 14.6-14.8& 14.8-15\\ \text{Frequency}& 2& 4& 5& 71& 48& 20\end{array}$

The number of athletes who completed the race in less than 14.6 s is ___ .

1. 11
2. 71
3. 82
4. 130

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

Q.

Which measure of central tendency is not a good representative of the data when you have a few extreme values?

1. Mean
2. Median
3. Mode
4. Ogive

Q.

The median for grouped data is formed by using the formula:

1. L + ( ) h

2. L - ( ) h.

3. L +

4. L + ( ) h.

Q.

Find the mode & median of the following frequency distribution:

1. 15, 12

2. 14, 12

3. 14, 12.6

4. 15, 12.6

5. 15, 13

6. 14, 13