Mean, Median And Mode

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Mean


Purpose

To calculate the arithmetic mean of all data measurements. It is the most representative descriptive measure of the central tendency of the data from a population or a sample. It has the advantage of lending itself to many other statistical calculations.


Anatomy

measures of location, mean

Reference: Juran's Quality Control Handbook

Terminology

A - The symbol - pronounced "X BAR".

B - The summation symbol, from i = 1 to n.

C - Represents the ith value of X.

D - Expresses the arithmetic mean/average of a sample of the population. It is the sum of data divided by the number of values in the data set. Expressed algebraically:

formula for the mean

Major Considerations

One must be careful when there are extreme values in the data set. It best represents the central tendency when the data is more or less evenly distributed about the middle, such as in the Normal data.

Application Cookbook

1. Using Excel - we have to use the function AVERAGE with data or range of data.

2. Another tool can be used in Minitab as described below: STAT>BASIC STATISTICS>DESCRIPTIVE STATISTICS

Median


Purpose

To calculate the half way point of the data measurements. This is one of three principal measurements of the central tendency of a population or a sample.

Anatomy

measure of location, median

Reference: Juran's Quality Control Handbook

Terminology

A - Represents the value at (n +1)/2 observation of the sample.

B - Represents the mean of the values at the (n/2) and (n/2 + 1) observations of the sample.

Where n = the number of observations in the sample.


Major Considerations

The median describes the central tendency of the data set and is sometimes a better measure of central tendency than the mean, especially for data coming from a non symmetrical distribution. It is less precise than the mean for data coming from a interval scales, for example from a measuring instrument.

Application Cookbook

1. Using Excel to calculate the arithmetic median of a data set, we have to use statistical function MEDIAN with data range.

2. Another tool to use of Minitab in described below: STAT>BASIC STATISTICS>DESCRIPTIVE STATISTICS

Mode


Purpose

To find the most frequently observed value in a set of data. This is one of three principal measurements of the central tendency of a population or a sample when data is coming from a nominal scale of measure.

It is also used for severely skewed distributions, for describing an irregular situation or for eliminating the effects of extreme values.

Anatomy

measures of location, mode

Reference: Juran's Quality Control Handbook

Terminology

A. Set of observed data.

B. The most frequently occurring value in the set of data.

C. Histogram, as processed by Minitab.

From Mean to Six Sigma Tools.

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