Measures of Central Tendency - Median

A median is a positional number that determines the position of the middle set of data. It divides the set of data into two parts. One part comprises all the values greater than or equal to the median and the other part comprises all the values smaller than or equal to the median.

In simple words, the median is the middle value when a data set is organised according to the magnitude. The value of the median remains unchanged if the size of the largest value increases because it is defined by the position of various values.

To evaluate the median, the values must be arranged in the sequence of numbers, and the numbers should be arranged in the value order starting from the lowest to the highest. For instance, while evaluating the median, if there is any sort of odd amount of numbers in the list, then the median will be the middle number with a similar number presented below or above.

However, if the amount is an even number, then the middle pair must be evaluated, combined together, and divided by two to find the median value.

Meaning, Merits, and Demerits of Median

Q.1. What is median?         “A median is that value of the data which divides the group into two equal parts, one part comprising all the values greater than the median and the other comprising the values less than the median.”….L.R. Connor

        Median is the middle value of the series when items are arranged either in an ascending or a descending order.

It divides the series into two equal parts. One part comprises all the values greater than the median and the other part comprises all the values smaller than the median.

 

Q.2. Explain the merits and demerits of median.
Answer:

(A) Some merits of median are:

(1) Easy to calculate and understand         It is easy to calculate and simple to understand.

        In many situations, the median can be located simply by inspection.

(2) Not affected by extreme values         It is not affected by the extreme values, i.e., the largest and smallest values because it is a positional average and not dependent on magnitude.
(3) Rigidly defined         It has a definite and certain value because it is rigidly defined.
(4) Best average in case of qualitative data         Median is the best measure of central tendency when we deal with qualitative data, where ranking is preferred instead of measurement or counting.
(5) Useful in case of an open-ended distribution         It can be calculated even if the values of the extremes are not known. However, the number of items should be known.
(6) Represented graphically         Its value can be determined or represented graphically with the help of ogive curves. Whereas, it is not possible in case of an arithmetic mean.
(B) Some demerits of median are:
(1) Arrangement of data is necessary         Since the median is an average position, arranging the data in ascending or descending order of magnitude is time-consuming in case of a large number of observations.
(2) Not based on all the observations         It is a positional average and does not consider the magnitude of the items.

        It neglects the extreme values.

(3)  Not a representative of the universe

 

        It is not dependent on all the observations, so it cannot be considered as their good representative.

        In case there is a big variation between the data, it will not be able to represent the data.

(4) Affected by fluctuations in sampling         It is affected by the fluctuations in sampling and this effect is more than that in case of an arithmetic mean.
(5) Lack of further algebraic treatment         It is a positional average, so further algebraic treatment is not possible. Example: We cannot compute the combined median of two groups of data.

 

Q.3. List some properties of median..
Answer:
Properties of median
  1. The sum of deviations of items from the median, ignoring the signs, is minimum.
  2. Median is a positional average, hence it is not influenced by the extreme values.

 

Q.4. Define partitional values. What is meant by first, second, and third quartile?
Answer:
(A) Partitional values Partition values are the values that are obtained by dividing a series into more than two parts.
(B) Quartiles
Types with their meaning         A quartile divides a series into four equal parts.

        For any series, there will be three quartiles.

        First quartile is also known as the lower quartile (Q1).

It divides the distribution in such a way that one-fourth (25%) of the total items fall below it and three-fourth (75%) are above it.

        Second quartile (Q2) or Median: It divides the distribution in two equal halves.

        Third quartile is also known as the upper quartile (Q3).

It divides the distribution in such a way that three-fourth (75%) of the total items fall below it and one-fourth (25%) are above it.

Multiple Choice Questions

Q.1. The ________ is that value of data which divides the group into two equal parts.
a. Mean

b. Mode

c. Median

d. Both (a) and (c)

Q.2. Which of the following is the merit of the median value of data?
a. Easy to calculate and simple to understand

b. Rigidly defined

c. Not affected by extreme values

d. All of the above

Q.3. Which of the following is the demerit of the median value of data?
a. Arrangement of data is mandatory

b. Affected by fluctuation in sampling

c. Lack of further algebraic treatment

d. All of the above

Q.4. Median _______ extreme values.
a. Includes

b. Does not include

c. Rejects

d. None of the above

Q.5. Median is not dependent upon which of the following criteria?
a. All the observations

b. Extreme values

c. Least value

d. All of the above

 

Answer Key
1 – a., 2 – d., 3 – d., 4 – b., 5 – d.

The above-mentioned is the concept that is elucidated in detail about the measures of central tendency – median for Class 11 Commerce students. To know more, stay tuned to our website.

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