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Chapter 3: Measures of Central Tendency
In the previous chapter, you have read about the tabular and graphic representation of the data. In this chapter, you will study the measures of central tendency which is a numerical method to explain the data in brief.
You can see examples of summarising a large set of data in day-to-day life, like average marks obtained by students of a class in a test, average rainfall in an area, average production in a factory, average income of persons living in a locality or working in a firm, etc.
Baiju is a farmer. He grows food grains in his land in a village called Balapur in Buxar district of Bihar. The village consists of 50 small farmers. Baiju has 1 acre of land. You are interested in knowing the economic condition of small farmers of Balapur. You want to compare the economic condition of Baiju in Balapur village.
For this, you may have to evaluate the size of his land holding, by comparing with the size of land holdings of other farmers of Balapur. You may like to see if the land owned by Baiju is –
1. above average in ordinary sense (see the Arithmetic Mean)
2. above the size of what half the farmers own (see the Median)
3. above what most of the farmers own (see the Mode) In order to evaluate Baiju’s relative economic condition, you will have to summarise the whole set of data of land holdings of the farmers of Balapur. T
his can be done by the use of central tendency, which summarises the data in a single value in such a way that this single value can represent the entire data. The measuring of central tendency is a way of summarising the data in the form of a typical or representative value.
There are several statistical measures of central tendency or “averages”.
The three most commonly used averages are:
• Arithmetic Mean
• Mode You should note that there are two more types of averages i.e. Geometric Mean and Harmonic Mean, which are suitable in certain situations. However, the present discussion will be limited to the three types of averages mentioned above.
Measures of central tendency or averages are used to summarise the data. It specifies a single most representative value to describe the data set. Arithmetic mean is the most commonly used average. It is simple to calculate and is based on all the observations. But it is unduly affected by the presence of extreme items.
Median is a better summary for such data. Mode is generally used to describe the qualitative data. Median and mode can be easily computed graphically. In case of open-ended distribution they can also be easily computed. Thus, it is important to select an appropriate average depending upon the purpose of analysis and the nature of the distribution.
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NCERT Solutions Class 11 Statistics Chapter 5 Measures of Central Tendency
Which average would be suitable in the following cases?
(i) Average size of readymade garments.
(ii) Average intelligence of students in a class.
(iii) Average production in a factory per shift.
(iv) Average wages in an industrial concern.
(v) When the sum of absolute deviations from average is least.
(vi) When quantities of the variable are in ratios.
(vii) In case of open-ended frequency distribution.
(i) Mode Average size of any ready made garments should be the size for which demand is the maximum. Hence, the modal value which represents the value with the highest frequency should be taken as the average size to be produced.
(ii) Median It is the value that divides the series into two equal parts. Therefore, Median will be the best measure for calculating the average intelligence of students in a class as it will give the average intelligence such that there are equal number of students above and below this average. It will not be affected by extreme values.
(iii) Arithmetic Mean The average production in a factory per shift is best calculated by Arithmetic Mean as it will capture all types of fluctuations in production during the shifts.
(iv) Arithmetic Mean Arithmetic Mean will be the most suitable measure. It is calculated by dividing the sum of wages of all the workers by the total number of workers in the industrial concern. It gives a fair idea of average wage bill taking into account all the workers.
(v) Arithmetic Mean The algebraic sum of the deviations of values about Arithmetic Mean is zero. Hence, when the sum of absolute deviations from average is the least, then mean could be used to calculate the average.
(vi) Median Median will be the most suitable measure in case the variables are in ratios as it is least affected by the extreme values.
(vii) Median Median is the most suitable measure as it can be easily computed even in case of open ended frequency distribution and will not get affected by extreme values.
Indicate the most appropriate alternative from the multiple choices provided against each question.
(i) The most suitable average for qualitative measurement is
(a) Arithmetic mean
(d) Geometric mean
(e) None of these
(b) Median is the most suitable average for qualitative measurement because Median divides a series in two equal parts thus representing the average qualitative measure without being affected by extreme values.
(ii) Which average is affected most by the presence of extreme items?
(c) Arithmetic Mean
(d) Geometric Mean
(e) Harmonic Mean
(c) It is defined as the sum of the values of all observations divided by the number of observations and therefore it is. affected the most by extreme values.
(iii) The algebraic sum of deviation of a set of n values from AM is
(d) None of these
(b) This is one of the mathematical properties of arithmetic mean that the algebraic sum of deviation of a set of n values from AM is zero.
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