Module 1_Theory.pdf
- 1. MODULE 1 – DESCRIPTIVE STATSTICS Prof. Suhas Patel STATISTICS FOR MANAGERS – 22MBA14 1 1. MEASURES OF CENTRAL TENDENCY OR AVERAGES Definition: According to Crum & Smith, “An average is sometimes called a measure of central tendency because individual values of variables cluster it.” Central Tendency is a statistical measure that determines a single value that accurately describes the center of the distribution of scores VARIOUS MEASURES OF CENTRAL TENDENCY 1) Arithmetic Mean or Mean 2) Geometric Mean 3) Harmonic Mean 4) Median 5) Quartiles 6) Deciles 7) Percentiles 8) Mode
- 2. MODULE 1 – DESCRIPTIVE STATSTICS Prof. Suhas Patel STATISTICS FOR MANAGERS – 22MBA14 2
- 3. MODULE 1 – DESCRIPTIVE STATSTICS Prof. Suhas Patel STATISTICS FOR MANAGERS – 22MBA14 3 1) ARITHMETIC MEAN OR MEAN (M) The arithmetic mean (or mean or average) is the most commonly used and readily understood measure of central tendency. In statistics, the term average refers to any of the measures of central tendency. The arithmetic mean is defined as being equal to the sum of the numerical values of each and every observation divided by the total number of observations Merits of Arithmetic Mean a) It is easy to understand and calculate. b) It is based on all the observation of the series. c) It is least affected by fluctuations of sampling. d) It is a calculated value. e) It is suitable for further mathematical treatment. Demerits of Arithmetic Mean a. It can give a risible result. b. it is affected by extreme points. c. It cannot be picked up by observation. d. It cannot be calculated for the problem related to open and classes. e. It cannot be used if we are dealing with qualitative characteristics which cannot be measured qualitatively. f. It cannot be obtained even if a single observation is mission or lost. Unless we drop it out and calculate mean using remaining values. MEDIAN (Md) The observation of a data that divides the whole data into two equal parts is called its median. According to Cantor, "the median is that value of the variable which divides the group into two equal parts, one part comprising all the values greater and other all values less than the median."
- 4. MODULE 1 – DESCRIPTIVE STATSTICS Prof. Suhas Patel STATISTICS FOR MANAGERS – 22MBA14 4 Merits of median • It is easy and simple to calculate. • It is rigidly defined. • It is located by a graph. • It is used for qualitative data. • It is computed for open-end classes. Demerits of median • The arrangement of data according to order is necessary. • It is not based on all the observation. • It cannot be determined exactly for ungrouped data. • it is affected by the fluctuation of data. MODE (Mo) Mode of data is that item or value of a variable which repeats the largest number of time. We have defined mode as the element which has the highest frequency in a given data set. In grouped data, we can find two kinds of mode: the Modal Class, or class with the highest frequency and the mode itself, Merits of mode • It is easy to calculate. • It is simple to understand. • It is not affected by extreme values. • It can be obtained by inspection or graph.
- 5. MODULE 1 – DESCRIPTIVE STATSTICS Prof. Suhas Patel STATISTICS FOR MANAGERS – 22MBA14 5 Demerits of mode • It is not rigidly defined. • It is not based on all observation. • It is affected by the fluctuation of sampling. • It is not suitable for further mathematical treatment. EMPIRICAL RELATION BETWEEN MEAN, MEDIAN AND MODE A distribution in which the values of mean, median and mode coincide (i.e. mean = median = mode) is known as a symmetrical distribution. Conversely, when values of mean, median and mode are not equal the distribution is known as asymmetrical or skewed distribution. In moderately skewed or asymmetrical distribution a very important relationship exists among these three measures of central tendency. MODE = 3 MEDIAN - 2 MEAN MEASURES OF DISPERSION: VARIOUS MEASURES OF DISPERSION 1) Range 2) Quartile Deviation 3) Mean Deviation 4) Standard Deviation/ Variance/ Coefficient of Variation 5) Lorenz Curve
- 6. MODULE 1 – DESCRIPTIVE STATSTICS Prof. Suhas Patel STATISTICS FOR MANAGERS – 22MBA14 6 STANDARD DEVIATION: Its symbol is σ (the Greek letter sigma) Standard deviation is a measure of the dispersion of a set of data from its mean. It is calculated as the square root of variance by determining the variation between each data point relative to the mean. If the data points are further from the mean, there is higher deviation within the data set. Description: The concept of Standard Deviation was introduced by Karl Pearson in 1893. It is by far the most important and widely used measure of dispersion. Its significance lies in the fact that it is free from those defects which afflicted earlier methods and satisfies most of the properties of a good measure of dispersion. Standard Deviation is also known as root-mean square deviation as it is the square root of means of the squared deviations from the arithmetic mean Merits of Standard Deviation: Among all measures of dispersion Standard Deviation is considered superior because it possesses almost all the requisite characteristics of a good measure of dispersion. It has the following merits: 1) It is rigidly defined. 2) It is based on all the observations of the series and hence it is representative. 3) It is amenable to further algebraic treatment. 4) It is least affected by fluctuations of sampling. Demerits: 1) It is more affected by extreme items. 2) It cannot be exactly calculated for a distribution with open-ended classes. 3) It is relatively difficult to calculate and understand.
- 7. MODULE 1 – DESCRIPTIVE STATSTICS Prof. Suhas Patel STATISTICS FOR MANAGERS – 22MBA14 7 COEFFICIENT OF VARIATION The coefficient of variation (CV) is a measure of relative variability. It is the ratio of the standard deviation to the mean (average). Definition: According to Karl Pearson who suggested this measure, “coefficient of variation is the percentage variation in mean, standard deviation being considered as the total variation in the mean.” For example, the expression “The standard deviation is 15% of the mean” is a CV. The CV is particularly useful when you want to compare results from two different surveys or tests that have different measures or values. For example, if you are comparing the results from two tests that have different scoring mechanisms. If sample A has a CV of 12% and sample B has a CV of 25%, you would say that sample B has more variation, relative to its mean. Formula: The formula for the coefficient of variation is: Coefficient of Variation = (Standard Deviation / Mean) * 100. In symbols: CV = (SD/ ) * 100. Merits- 1)It represents the ratio of the standard deviation to the mean 2)Compares variation from one distribution to another. 3)It's unitless and dimensionless variable Demerits- 1)It can't be used directly to construct confidence intervals for mean 2)It approaches to infinity when mean is close to zero