CBSE Class 11 Economics Measures Of Central Tendency Notes

UNIT – 3

STATISTICAL TOOLS AND INTERPRETATION 

1. Measures of central Tendency.

2. Measures of Dispersion

3. Co-relation and Measures of correlation

4. Introduction to Index Numbers.

Measures of Central Tendency

(Important Terms & Concepts) :-

1. Average or measures of central Tendency :- It is a value which is a typical or representative of a set of data. Averages are also called measures of central tendency, since they tend to lie centrally, with in a set of data arranged according to magnitude.

2. Functions of Average :-

√ Average helps to get a representative value to the entire set of data.

√ It Facilitates Comparison.

√ It is a useful tool in decision- making.

3. Essentials of a Good Average / good measures of Central Tendency : -

√ Simplicity in calculation

√ Easy to understand

√ Rigidly Defined

√ Precise Value

√ Based upon all observations

√ Unaffected by extreme values.

√ Capable for further statistical calculations.

4. Types of Averages / measures of central Tendency :- There are three averages, which are in common use- Arithmetic Mean, Median and Mode.

5. Arithmetic Means ( X ):- It is the most common type of measures of central tendency. It is obtained by dividing the sum of all observations in a series by the total numbers of observations.

6. Calculation of Arithmetic Mean :-

For Individual series / ungrouped Data :- 

8. Merits of Arithmetic Mean:-

(i) It is easy to calculate and simple to understand.

(ii) It is rigidly defined.

(iii) It is a calculated value not a positional value.

(iv) It is based on all observations

9. Demerits of Arithmetic Mean:-

• It is affected by presence of extreme values

•  It cannot be calculated in open-ended series

•  It cannot be ascertained graphically.

•  It sometimes gives misleading and surprising results.

10. MEDIAN:-

It is defined as the middle value of the series when the data is arranged in ascending or descending order. In other words, median is that value of the distribution which divides the group into two equal parts, one part comprising all greater values and the other comprising values less than the median.

12. Merits of median :-

⇒ It is easy to understand and easy to compute.

⇒ It is not unduly affected by extreme observations

⇒ Median can be located graphically with the help of ogives.

⇒ It is the most appropriate average in case of open-ended classes.

⇒ It is the most suitable average for qualitative measurement such as intelligence, beauty etc.

⇒ It is a positional value and not a calculated value.

13. Demerits of Median

(I) It is not based on all observations of the series since it is a positional average.

(II) It requires arrangement of data, but other averages do not need it.

(III) It can not be computed exactly where the number of items in a series is even.

14. Related Measures Of Median- Quartiles & Percentiles:-

Quartiles are the measures which divide the data into four equal parts, each part contains equal number of observations. There are three quartiles - Q1, Q2, and Q3. The 1st quartile denoted by Q1 is called lower quartile and 25% of the item of the distribution are below it and 75% of the items are greater than it.

The second quartile is known as median and is denoted by Q2. It has 50% of the item above it. The third Quartile is known as Q3 and it is also called upper Quartile and 75% of the items are below it and 25% of the items are above it. Thus , Q1 and Q3 denote the two items with which central 50% of item lie.

Percentiles divide the series into hundred equal parts. For any series, there are 99 percentiles denoted by P1, P2, P3,……, P99. P50 is the median value.

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