# Arithmetic Mean and Data

1) WHY IT IS NECESSARY TO SUMMARISE DATA? EXPLAIN THE APPROACHES AVAILABLE TO SUMMARIZE THE DATA DISTRIBUTIONS?

➢ Graphical representation is a good way to represent summarised data. However, graphs provide us only an overview and thus may not be used for further analysis. Hence, we use summary statistics like computing averages. to analyse the data. Mass data, which is collected, classified, tabulated and presented systematically, is analysed further to bring its size to a single representative figure. This single figure is the measure which can be found at central part of the range of all values. It is the one which represents the entire data set. Hence, this is called the measure of central tendency.

In other words, the tendency of data to cluster around a figure which is in central location is known as central tendency. Measure of central tendency or average of first order describes the concentration of large numbers around a particular value. It is a single value which represents all units.

a. Statistical Averages: The commonly used statistical averages are arithmetic mean, geometric mean, harmonic mean.

b. Arithmetic mean is defined as the sum of all values divided by number of values and is represented by X.

c. Median: Median of a set of values is the value which is the middle most value when they are arranged in the ascending order of magnitude. Median is denoted by ‘M’.

d. Mode: Mode is the value which has the highest frequency and is denoted by Z. Modal value is most useful for business people. For example, shoe and readymade garment manufacturers will like to know the modal size of the people to plan their operations. For discrete data with or without frequency, it is that value corresponding to highest frequency.

Appropriate Situations for the use of Various Averages 1. Arithmetic mean is used when:

a. In depth study of the variable is needed

b. The variable is continuous and additive in nature

c. The data are in the interval or ratio scale

d. When the distribution is symmetrical

2. Median is used when:

a. The variable is discrete

b. There exists abnormal values

c. The distribution is skewed

d. The extreme values are missing

e. The characteristics studied are qualitative

f. The data are on the ordinal scale

3. Mode is used when:

a. The variable is discrete

b. There exists abnormal values

c. The distribution is skewed

d. The extreme values are missing

e. The characteristics studied are qualitative

4. Geometric mean is used when:

a. The rate of growth, ratios and percentages are to be studied b. The variable is of multiplicative nature

5. Harmonic mean is used when:

a. The study is related to speed, time

b. Average of rates which produce equal effects has to be found

Positional Averages

Median is the mid-value of series of data. It divides the distribution into two equal portions. Similarly, we can divide a given distribution into four, ten or hundred or any other number of equal portions.

2) EXPLAIN THE PURPOSE OF TABULAR PRESENTATION OF STATISTICAL DATA. DRAFT A FORM OF TABULATION TO SHOW THE DISTRIBUTION OF POPULATION ACCORDING TO i) Community by age, ii) Literacy, iii) Sex, and iv) Marital Status?

➢ Tabulation follows classification. It is a logical or systematic listing of related data in rows and columns. The row of a table represents the horizontal arrangement of data and column represents the vertical arrangement of data. The presentation of data in tables should be simple, systematic and unambiguous. The following are the objectives and purpose of tabular presentation of statistical data.

a) It simplifies complex data

b) It highlights important characteristics

c) It presents...

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