Math՚s: Measures of Central Tendency: Median and Calculation of Median (For CBSE, ICSE, IAS, NET, NRA 2022)

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Median- Meaning

  • Median is a measure of central tendency which gives the value of the middle-most observation in the data when the data is arranged in ascending (or descending) order. Median is denoted by .
  • Median divides the data into two equal parts, wherein half of the values lie below the median and half of the values lie above the median.

Calculation of Median

Individual Series

  • In an individual series, we go through the following steps to work out median-
  • Arrange the series in ascending or descending order.
  • When the series has an odd number of observations, observation is median
  • When the series has an even number of observations, Median is worked out by the following formula-

Example- Calculate the median of the series 9, 10, 5, 11, 8, 22, 15, 18,17, 13.

Solution- Firstly, the observations will be arranged in an ascending order as follows

5.8, 9, 10, 11, 13, 15, 17,18, 22

Since the series has an even number of observations i.e.. 10, the following formula will be applied to get the value of median-

Discrete Frequency Series

Follow the steps given below-

  • Arrange the data in ascending or descending order.
  • Find cumulative frequencies
  • Find the value of middle term by using the formula-
  • Find that cumulative frequency which is nearer to i.e.. equal to or greater than
  • Locate the observation that corresponds to the above cumulative frequency. This is the value of the median.

Example- Find the median from the following

Find the Median from the Following
Size10121520
Frequency26102

Solution-

Find the Median from the Following
SizeFrequencyCumulative Frequency
1022
1268
151018
20220

As lies in cumulative frequency , Median will be .

Interval Series

In case of interval series, cumulative frequencies are taken and then the median class is located using the formula . The class that corresponds to the cumulative frequency which is nearer to is the median class. The values related to the median class are taken and substituted in the following formula to obtain the value of median.

Where, lower limit of the median class; : Median number; : cumulative frequency of the class preceding the median class; : frequency of the median class; and : size of the class

Example- Find the median from the following

Find the Median from the Following
Class Interval0 - 55 - 1010 - 1515 - 20
Frequency2486

Solution

Find the Median from the Following
Class IntervalFrequencyCumulative Frequency
0 - 522
5 - 1046
10 - 15814
15 - 20620

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