Median for Ungrouped Data

Q.

The following observations are arranged in ascending order. The median of the data is $25.$ Find the value of $x.$

$17,x,24,x+7,35,36,46$

1. $25$

2. $18$

3. $17$

4. $35$

Q.

The maximum bowling speeds, in $kmperhour,$, of $33$ players at a cricket coaching centre are given as follows: Speed $(km/h)85-100,100-115,115-130,130-145$ Number of players $11,9,8,5$. Calculate the median of bowling speed.

Q.

The medians for the first 7 natural numbers (1, 2, 3, 4, 5, 6, 7) and the first 6 natural numbers (1, 2, 3, 4, 5, 6) respectively are _____ .

1. 3, 3.5
2. 4, 3.5
3. 4, 3
4. 4, 4

Q. The median of the following observations 11, 12, 14, (x - 2), (x + 4), (x + 9), 32, 38, 47 arranged in ascending order is 24. Find the value of x and hence find the mean. [4 MARKS]

Q. The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations in the set is
increased by 2, then the median of the new set

1. is decreased by 2
2. is two times the original median
3. s increased by 2
4. remains the same as that of the original set

Q. The numbers 6, 8, 10, 12, 13 and x are arranged in an ascending order. If the mean of the observations is equal to the median, find the value of x. [3 MARKS]

Q.

Find the mean of the data :

$20,17,48,25,29,18,35,27,42,30$

Q.

Question 13
Ten observations 6, 14, 15, 17, x+1, 2x – 13, 30, 32, 34 and 43 are written in an ascending order. The median of the data is 24. Find the value of x.

Q. Question 02.
In calculating the mean of grouped data, grouped in classes of equal width, we may use the formula,
$\overline{x}=a+\frac{\sum f_i{d}_i}{\sum f_i}$
where, a is the assumed mean, a must be one of the mid - point of classes. Is the last statement correct ? Justify your answer.

Q. A Mathematics aptitude test of 50 students was recorded as follows:
$\begin{array}{cc}Marks& No.ofStudents\\ 50-60& 4\\ 60-70& 8\\ 70-80& 14\\ 80-90& 19\\ 90-100& 5\end{array}$
Draw a histogram for the above data using a graph paper [4 MARKS]

Q. For an arranged data set, the median is the observation.

1. middle most
2. most common
3. least common

Q.

Which of the following is the median of a set of observations?

1. The average value of data set

2. The middle most point of data set

3. Twice the average value of data set

4. The most common data in a data set.

Q.

The age of 30 workers in a factory are as follows

$\begin{array}{cc}\text{Age}& \text{No. of workers}\\ 24& 5\\ 25& 7\\ 26& 8\\ 27& 4\\ 28& 6\end{array}$

(i) Find the mean, median and mode for the above ungrouped data. [4 MARKS]

Q.

The following table shows the marks obtained by 5 students in a classroom, find the average marks of the classroom.

$$\begin{array}{cc}Marks& Frequency\\ 98& 1\\ 65& 1\\ 88& 2\\ 54& 1\end{array}$$

1. 76.6

2. 78.6

3. 78.9

4. 77.6

Q.

Question 3
A life insurance agent found the following data for the distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 years.

$\begin{array}{cc}Age\left(inyears\right)& Numberofpolicyholders\\ Below20& 2\\ Below25& 6\\ Below30& 24\\ Below35& 45\\ Below40& 78\\ Below45& 89\\ Below50& 92\\ Below55& 98\\ Below60& 100\end{array}$

Q.

The measure of central tendency which we'll reject when the data contains some extreme values, is the median.

1. True

2. False

Q.

For the following set of numbers, find the median: [3 MARKS]
10, 75, 3, 81, 17, 27, 4, 48, 12, 47, 9, 15

Q. The median is that value of the given set of observations, which divides it into exactly two parts.

1. True
2. False

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. 30

3. 29

4. 40

Q.

There is a set of 7 natural numbers namely: 1, 2, 3, 4, 5, 6, 7. Another set of natural number are :1, 2, 3, 4, 5, 6. What are the values of medians in each set of numbers respectively?

1. 4, 3.5

2. 4, 4

3. 4, 3

4. 3, 3.5

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

$78,64,57,x-3,x-7,x-11,30,25,22,20$

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

1. 48
2. 48.5
3. 60
4. 50.5

Q.

The following table gives the marks scored by students in an exam.

$\begin{array}{cc}\text{Marks}& \text{No. of students}\\ \text{Above}0& 80\\ \text{Above}10& 77\\ \text{Above}20& 72\\ \text{Above}30& 65\\ \text{Above}40& 55\\ \text{Above}50& 43\\ \text{Above}60& 23\\ \text{Above}70& 16\\ \text{Above}80& 10\\ \text{Above}90& 8\\ \text{Above}100& 0\end{array}$

Find the mean for the following data using assumed mean method. [4 MARKS]

Q.

If the median of the following data is 50, then find p.
$$\begin{array}{cccccc}Class& \text{0-20}& \text{20-40}& \text{40-60}& \text{60-80}& \text{80-100}\\ Frequency& \text{10}& \text{7}& \text{16}& \text{p}& \text{8}\end{array}$$

1. 6

2. 7

3. 8

4. 9

Q.

Find the median of the following data.

$$\begin{array}{cccccc}Classinterval& 0-10& 10-20& 20-30& 30-40& 40-50\\ Frequency& 10& 9& 8& 17& 6\end{array}$$

Q.

Find the median term of the following cumulative frequency distribution:
$\begin{array}{ccc}x& \text{frequency}& \text{Cumulative frequency}\\ 22& 1& 1\\ 34& 2& 3\\ 39& 2& 5\\ 45& 8& 13\\ 54& 8& 21\\ 56& 9& 30\\ 68& 4& 34\\ 78& 4& 38\\ 84& 2& 40\end{array}$

1. 49.5

2. 53.5

3. 54

4. 55

Q.

A life insurance agent found the following data for the distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 years.

$\begin{array}{cc}Age\left(inyears\right)& Numberofpolicyholders\\ Below20& 2\\ Below25& 6\\ Below30& 24\\ Below35& 45\\ Below40& 78\\ Below45& 89\\ Below50& 92\\ Below55& 98\\ Below60& 100\end{array}$

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. Median and mean both are misleading for a given data set.

1. always
2. sometimes
3. most of the time

Q.

If the median of the following data is 50, then find p.
$\begin{array}{cccccc}Class& \text{0-20}& \text{20-40}& \text{40-60}& \text{60-80}& \text{80-100}\\ Frequency& \text{10}& \text{7}& \text{16}& \text{p}& \text{8}\end{array}$

1. 9

2. 6

3. 8

4. 7

Q. If the first term of an increasing sequence is decreased, the new median of this sequence will:

1. Increase
2. Remain same
3. Decrease
4. Become zero