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Central Tendency

Presented by

Sajjat Hossain SalimID: 120104635

KamrozzamanID: 120104508

Ali AshrafID: 120104505

Rasel ChowdhuryID:120104492

Course Outline

• Definition of central tendency• Definition of measures of central tendency• Objective of central tendency• Types of central tendency• Definition of Arithmetic mean, median with

merits, demerits

Central Tendency

• In general terms, central tendency is a statistical measure that determines a single value that accurately describes the center of the distribution and represents the entire distribution of scores.

Measures of Central Tendency

• A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data. As such, measures of central tendency are sometimes called measures of central location. The three most common measures of central tendency are the mean, the median, and the mode.

Objective of central tendency

• The goal of central tendency is to identify the single value that is the best representative for the entire set of data.

Types of central Tendency

• Mean • Median• Mode

Mean

• The mean is the most commonly used measure of central tendency.

• Computation of the mean requires scores that are numerical values measured on an interval or ratio scale.

• The mean is obtained by computing the sum, or total, for the entire set of scores, then dividing this sum by the number of scores.

Median

• If the scores in a distribution are listed in order from smallest to largest, the median is defined as the midpoint of the list.

• The median divides the scores so that 50% of the scores in the distribution have values that are equal to or less than the median.

• Computation of the median requires scores that can be placed in rank order (smallest to largest) and are measured on an ordinal, interval, or ratio scale.

Mode

• The mode is defined as the most frequently occurring category or score in the distribution.

• In a frequency distribution graph, the mode is the category or score corresponding to the peak or high point of the distribution.

• The mode can be determined for data measured on any scale of measurement: nominal, ordinal, interval, or ratio

Merits of mean

• It is easy to understand & easy to calculate. • It is not much affected by sampling

fluctuations. • It is capable of further mathematical

treatment. • It is based upon all values of the given data.

Demerits of Mean

• It cannot be calculated if any observations are missing.

• It cannot be calculated for the data with open end classes.

• It is affected by extreme values. • It cannot be located graphically. • It may be number which is not present in the data. • It can be calculated for the data representing

qualitative characteristic.

Merits of Median

• It is easy to understand and easy to calculate.• If the number of items is sufficiently large, it is more• accurate and more reliable.• It is a calculated value and is not based on its position

in the series.• It is possible to calculate even if some of the details of

the data are lacking.• Of all averages, it is affected least by fluctuations of

sampling.• It provides a good basis for comparison.

Demerits of Median

• It is not based upon all values of the given data.• For larger data size the arrangement of data in

the increasing order is difficult process. • It is not capable of further mathematical

treatment. • It is insensitive to some changes in the data

values.

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