Measures of central tendency
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This document discusses measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. The mean is the average value and is calculated by summing all values and dividing by the total number of values. The median is the middle value when values are arranged in order. The mode is the value that occurs most frequently. The document discusses when each measure is most appropriate to use and provides examples of calculating the mean, median, and mode. It also covers the properties, merits, and demerits of each measure of central tendency.
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Measures of central tendency
- 1. Measures of Central Tendency Dr. Suresh Kumar Murugesan Ph.D Yellow Pond
- 2. About the Presenter ● Dr.Suresh Kumar Murugesan is a Passionate Professor,Researcher and Positive Mental Health and Wellness Practitioner from Madurai, Tamil Nadu,India ● At present he is Heading the PG Department of Psychology,The American College,Madurai and Adjunct Professor of School of Behavioural Sciences and Education at Texila American University ● He is very keen in learning new research studies in behavioural Sciences and open to learn. ● His ultimate aim is to make impression in the field of Knowledge ● His area of specializations are Psychometry,Counselling & Psychotherapy Yellow Pond
- 3. Disclaimer ● This presentation is prepared for learning purpose only and all the images and pictures used in this presentation are taken from google image search. ● Due recognition was given to all the material collected from the various sources. ● Any name or reference is missed kindly bring it to the notice of the presenter for inclusion. ● Email - sureshkumar800@yahoo.com Thank you Yellow Pond
- 4. 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. Yellow Pond
- 5. Measures of Central Tendency Measures of central tendency are sometimes called measures of central location Yellow Pond
- 6. Summary of when to use the mean, median and mode Type of Variable Best measure of central tendency Nominal Mode Ordinal Median Interval/Ratio (not skewed) Mean Interval/Ratio (skewed) Median Yellow Pond
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- 21. Mean Yellow Pond
- 22. Definition: Average ● “A measure of central tendency is a typical value around which other figures congregate.” ● “An average stands for the whole group of which it forms a part yet represents the whole.” ● “One of the most widely used set of summary figures is known as measures of location.” Yellow Pond
- 23. Characteristics for a good or an ideal average The following properties should possess for an ideal average. 1. It should be rigidly defined. 2. It should be easy to understand and compute. 3. It should be based on all items in the data. 4. Its definition shall be in the form of a mathematical formula. 5. It should be capable of further algebraic treatment. 6. It should have sampling stability. 7. It should be capable of being used in further statistical computations or processing. Yellow Pond
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- 27. Arithmetic Mean - Shortcut method Yellow Pond
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- 48. Merits of Arithmetic Mean Yellow Pond
- 49. Merits of Arithmetic mean 1. It is rigidly defined. 2. It is easy to understand and easy to calculate. 3. If the number of items is sufficiently large, it is more accurate and more reliable. 4. It is a calculated value and is not based on its position in the series. 5. It is possible to calculate even if some of the details of the data are lacking. 6. Of all averages, it is affected least by fluctuations of sampling. 7. It provides a good basis for comparison. Yellow Pond
- 50. Demerits of Arithmetic Mean Yellow Pond
- 51. Demerits of Arithmetic mean 1. It cannot be obtained by inspection nor located through a frequency graph. 2. It cannot be in the study of qualitative phenomena not capable of numerical measurement i.e. Intelligence, beauty, honesty etc., 3. It can ignore any single item only at the risk of losing its accuracy. 4. It is affected very much by extreme values. 5. It cannot be calculated for open-end classes. 6. It may lead to fallacious conclusions, if the details of the data from which it is computed are not given. Yellow Pond
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- 85. Merits of Arithmetic Median Yellow Pond
- 86. Merits of Median 1. Median is not influenced by extreme values because it is a positional average. 2. Median can be calculated in case of distribution with open-end intervals. 3. Median can be located even if the data are incomplete. 4. Median can be located even for qualitative factors such as ability, honesty etc. Yellow Pond
- 87. Demerits of Arithmetic Median Yellow Pond Yellow Pond
- 88. Demerits of Median 1. A slight change in the series may bring drastic change in median value. 2. In case of even number of items or continuous series, median is an estimated value other than any value in the series. 3. It is not suitable for further mathematical treatment except its use in mean deviation. 4. It is not taken into account all the observations. Yellow Pond
- 89. Mode
- 90. Mode ● The mode refers to that value in a distribution, which occur most frequently. It is an actual value, which has the highest concentration of items in and around it. ● According to Croxton and Cowden “ The mode of a distribution is the value at the point around which the items tend to be most heavily concentrated. It may be regarded at the most typical of a series of values”. Yellow Pond
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- 93. Remarks : 1. If (2f1-f0-f2) comes out to be zero, then mode is obtained by the following formula taking absolute differences within vertical lines. Yellow Pond
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- 99. Mean, Median and Mode ● In a symmetrical distribution the three simple averages mean = median = mode. ● For a moderately asymmetrical distribution, the relationship between them are brought by Prof. Karl Pearson as ○ mode = 3 median - 2 mean. Yellow Pond
- 100. Mode Example : If the mean and median of a moderately asymmetrical series are 26.8 and 27.9 respectively, what would be its most probable mode? Solution: Using the empirical formula Mode = 3 median – 2 mean = 3 × 27.9 – 2 × 26.8 = 30.1 Yellow Pond
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- 102. Merits of Arithmetic Mode
- 103. Merits of Mode 1. It is easy to calculate and in some cases it can be located mere inspection 2. Mode is not at all affected by extreme values. 3. It can be calculated for open-end classes. 4. It is usually an actual value of an important part of the series. 5. In some circumstances it is the best representative of data. Yellow Pond
- 104. Demerits of Arithmetic Mode Yellow Pond
- 105. Demerits of mode 1. It is not based on all observations. 2. It is not capable of further mathematical treatment. 3. Mode is ill-defined generally, it is not possible to find mode in some cases. 4. As compared with mean, mode is affected to a great extent,by sampling fluctuations. 5. It is unsuitable in cases where relative importance of items has to be considered. Yellow Pond