Median of Raw Data
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 or descending order.
Step II: Observe the number of variates in the data. Let the number of variates in the data be n. Then
find the median as following.
(i) If n is odd then \(\frac{n + 1}{2}\)th variate is the
median.
(ii) If n is even then the mean of \(\frac{n}{2}\)th and (\(\frac{n}{2}\)
+ 1)th variates is the median, i.e.,
median = \(\frac{1}{2}\left \{\frac{n}{2}\textrm{th Variate}
+ \left (\frac{n}{2} + 1\right)\textrm{th Variate}\right \}\).
Solved Examples on Median of Raw Data or Median of Ungrouped Data:
1. Find the median of the ungrouped data.
15, 18, 10, 6, 14
Solution:
Arranging variates in ascending order, we get
6, 10, 14, 15, 18.
The number of variates = 5, which is odd.
Therefore, median = \(\frac{5 + 1}{2}\)th variate
=
3^{rd} variate
=
14.
2. Find the median of the raw data.
8, 7, 15, 12, 10, 8, 9
Solution:
Arranging the variates in ascending order, we get
7, 8, 8, 9, 10, 12, 15.
The number of variates = 7, which is odd.
Therefore, median = the \(\frac{7 + 1}{2}\)th variate
= 4^{th} variate
= 9.
3. Find the median of the ungrouped data.
10, 17, 16, 21, 13, 18, 12, 10.
Solution:
Arranging the variates in ascending order, we get
10, 17, 16, 21, 13, 18, 12, 10.
The number of variates = 8, which is even.
Therefore, median = mean of the \(\frac{8}{2}\)th and (\(\frac{8}{2}\) + 1)th variate
= mean of the 4^{th} and 5^{th }variates
= mean of 13 and 16
= (\(\frac{13 + 16}{2}\)
= (\(\frac{29}{2}\)
= 14.5.
4. Find the median of the raw data.
8, 7, 5, 6, 3, 8, 5, 3
Solution:
Arranging variates in descending order, we get
8, 8, 7, 6, 5, 5, 3, 3.
The number of variates = 8, which is even.
Therefore, median = mean of \(\frac{8}{2}\)th and (\(\frac{8}{2}\) + 1)th variate
= mean of 4^{th} and 5^{th} variate
= mean of 6 and 5
= \(\frac{6 + 5}{2}\)
= 5.5
Note: The median need not be form among the variates.
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 cumulativefrequency 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 cumulativefrequency table of the data. Step III: Select the cumulative

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,

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 Stepdeviation 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 cumulativefrequency 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 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.