Problems on Median of Raw Data
Median is another measure of central tendency of a
distribution. We will solve different types of problems on Median
of Raw Data.
Solved Examples on Median
of Raw Data:
1. The height (in cm) of
11 players of a team are as follows:
160, 158, 158, 159, 160,
160, 162, 165, 166, 167, 170.
Find the median height of
the team.
Solution:
Arrange the variates in the ascending order, we get
157, 158, 158, 159, 160, 160, 162, 165, 166, 167, 170.
The number of variates = 11, which is odd.
Therefore, median = \(\frac{11 + 1}{2}\)th variate
= \(\frac{12}{2}\)th variate
= 6th variate
= 160.
2. Find the median of the
first five odd integers. If the sixth odd integer is also included, find the
difference of medians in the two cases.
Solution:
Writing the first five odd
integers in ascending order, we get
1, 3, 5, 7, 9.
The number of variates =
5, which is odd.
Therefore, median = \(\frac{5
+ 1}{2}\)th variate
= \(\frac{6}{2}\)th
variate
= 3th variate
= 5.
When the sixth integer is
included, we have (in ascending order)
1, 3, 5, 7, 9, 11.
Now, the number of
variates = 6, which is even.
Therefore, median = mean of
the \(\frac{6}{2}\)th and (\(\frac{6}{2}\) + 1)th variate
= mean of the 3th and 4th variates
= mean of 5 and 7
= (\(\frac{5 + 7}{2}\)
= (\(\frac{12}{2}\)
= 6.
Therefore, the difference of medians in the two cases = 6 – 5 = 1.
3. If the median of 17, 13, 10, 15, x happens to be the integer x
then find x.
Solution:
There are are five (odd) variates.
So, \(\frac{5 + 1}{2}\)th variate, i.e., 3rd
variate when written in the ascending order will the medina x.
So, the variates in ascending order should be 10,
13, x, 15, 17.
Therefore, 13 < x < 15.
But x is an integer.
So, x = 14.
4. Find the median of the collection of the first seven
whole numbers. If 9 is also included in the collection, find the difference of
the medians in the two cases.
Solution:
The first seven whole numbers arranged in ascending order
are
0, 1, 2, 3, 4, 5, 6.
Here, the total number of variates = 7, which is odd.
Therefore, \(\frac{7 +
1}{2}\)th, i.e., 4th variate is the median.
So, median = 3.
When 9 is included in the
collection, the variates in the ascending order are
0, 1, 2, 3, 4, 5, 6, 9.
Here the number of variates = 8, which is even.
Therefore, median = mean
of the \(\frac{8}{2}\)th variate and the (\(\frac{8}{2}\) + 1)th variate
= Mean of the 4th
variate and the 5th variate
= mean of 3 and 4
= \(\frac{3 +
4}{2}\)
= \(\frac{7}{2}\)
= 3.5.
Therefore, the difference
of medians = 3.5 – 3 = 0.5
5. If the numbers 25, 22,
21, x + 6, x + 4, 9, 8, 6 are in order and their median is 16, find the value
of x.
Solution:
Here, the number of
variates = 8 (in descending order).
8 is even.
Therefore, median = mean
of the \(\frac{8}{2}\)th variate and the (\(\frac{8}{2}\) + 1)th variate
= Mean of the 4th
variate and the 5th variate
= Mean of x + 6 and x +
4
= \(\frac{(x + 6) + (x
+ 4)}{2}\)
= \(\frac{x + 6 + x +
4}{2}\)
= \(\frac{2x + 10}{2}\)
= \(\frac{2(x +
5)}{2}\)
= x + 5.
According to the problem,
x + 5 = 16
⟹ x = 16 - 5
⟹ x = 11.
6. The marks obtained by 20 students in a class test are given below.
Find the median of marks
obtained by the students.
Solution:
Arranging the variates in
ascending order, we get
6, 6, 6, 6, 6, 7, 7, 7, 7,
7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10.
The number of variates =
20, which is even.
Therefore, median = mean of
\(\frac{20}{2}\)th and (\(\frac{20}{2}\) + 1)th variate
= mean of the 10th and 11th variates
= mean of 7 and7
= (\(\frac{7 + 7}{2}\)
= (\(\frac{14}{2}\)
= 7.
You might like these
-
In worksheet on estimating median and the quartiles using ogive we will solve various types of practice questions on measures of central tendency. Here you will get 4 different types of questions on estimating median and the quartiles using ogive.1.Using the data given below
-
In worksheet on finding the quartiles and the interquartile range of raw and arrayed data we will solve various types of practice questions on measures of central tendency. Here you will get 5 different types of questions on finding the quartiles and the interquartile
-
In worksheet on finding the median of arrayed data we will solve various types of practice questions on measures of central tendency. Here you will get 5 different types of questions on finding the median of arrayed data. 1. Find the median of the following frequency
-
For a frequency distribution, the median and quartiles can be obtained by drawing the ogive of the distribution. Follow these steps. Step I: Change the frequency distribution into a continuous distribution by taking overlapping intervals. Let N be the total frequency.
-
In worksheet on finding the median of raw data we will solve various types of practice questions on measures of central tendency. Here you will get 9 different types of questions on finding the median of raw data. 1. Find the median. (i) 23, 6, 10, 4, 17, 1, 3 (ii) 1, 2, 3
-
If in a continuous distribution the total frequency be N then the class interval whose cumulative frequency is just greater than \(\frac{N}{2}\) (or equal to \(\frac{N}{2}\)) is called the median class. In other words, median class is the class interval in which the median
-
The variates of a data are real numbers (usually integers). So, thay are scattered over a part of the number line. An investigator will always like to know the nature of the scattering of the variates. The arithmetic numbers associated with distributions to show the nature
-
Here we will learn how to find the quartiles for arrayed data. Step I: Arrange the grouped data in ascending order and from a frequency table. Step II: Prepare a cumulative-frequency table of the data. Step III:(i) For Q1: Select the cumulative frequency that is just greater
-
If the data are arranged in ascending or descending order then the variate lying at the middle between the largest and the median is called the upper quartile (or the third quartile), and it denoted by Q3. In order to calculate the upper quartile of raw data, follow these
-
The three variates which divide the data of a distribution in four equal parts (quarters) are called quartiles. As such, the median is the second quartile. Lower quartile and the method of finding it for raw data: If the data are arranged in ascending or descending order
-
To find the median of arrayed (grouped) data we need to follow the following steps: Step I: Arrange the grouped data in ascending or descending order, and form a frequency table. Step II: Prepare a cumulative-frequency table of the data. Step III: Select the cumulative
-
The median of raw data is the number which divides the observations when arranged in an order (ascending or descending) in two equal parts. Method of finding median Take the following steps to find the median of raw data. Step I: Arrange the raw data in ascending
-
In worksheet on finding the mean of classified data we will solve various types of practice questions on measures of central tendency. Here you will get 9 different types of questions on finding the mean of classified data 1.The following table gives marks scored by students
-
In worksheet on finding the mean of arrayed data we will solve various types of practice questions on measures of central tendency. Here you will get 12 different types of questions on finding the mean of arrayed data.
-
In worksheet on finding the mean of raw data we will solve various types of practice questions on measures of central tendency. Here you will get 12 different types of questions on finding the mean of raw data. 1. Find the mean of the first five natural numbers. 2. Find the
-
Here we will learn the Step-deviation method for finding the mean of classified data. We know that the direct method of finding the mean of classified data gives Mean A = \(\frac{\sum m_{i}f_{i}}{\sum f_{i}}\) where m1, m2, m3, m4, ……, mn are the class marks of the class
-
Here we will learn how to find the mean from graphical representation. The ogive of the distribution of marks of 45 students is given below. Find the mean of the distribution. Solution: The cumulative-frequency table is as given below. Writing in overlapping class intervals
-
Here we will learn how to find the mean of classified data (continuous & discontinuous). If the class marks of the class intervals be m1, m2, m3, m4, ……, mn and the frequencies of the corresponding classes be f1, f2, f3, f4, .., fn then the mean of the distribution is given
-
The mean of data indicate how the data are distributed around the central part of the distribution. That is why the arithmetic numbers are also known as measures of central tendencies. Mean Of Raw Data: The mean (or arithmetic mean) of n observations (variates)
-
If the values of the variable (i.e., observations or variates) be x\(_{1}\), x\(_{2}\), x\(_{3}\), x\(_{4}\), ....., x\(_{n}\) and their corresponding frequencies are f\(_{1}\), f\(_{2}\), f\(_{3}\), f\(_{4}\), ....., f\(_{n}\) then the mean of the data is given by
9th Grade Math
From Problems on Median of Raw Data to HOME PAGE
Didn't find what you were looking for? Or want to know more information
about Math Only Math.
Use this Google Search to find what you need.
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.