“Use of Central Tendency and Dispersion in Business Decision” Course Title: Business Statistics
Course Code: STS201
Submitted To: Mr. Raihanul Hasan
Date of submission: 26-12-12
STATE UNIVERSITY OF BANGLADESH
We can use single numbers called “Summary Statistics’ to describe characteristics of a data set. Two of these characteristics are particularly important to decision makers: 1. Central tendency
Measures of central tendency and dispersion provide a convenient way to describe and compare sets of data.
Central tendency is the middle point of a distribution. Measures of central tendency are also known as Measures of location. Measures of central tendency yield information about the center, or middle part, of a group of a numbers. It does not focus on the span of data set or how far values are from the middle numbers.
Dispersion is the spread of the data in a distribution, that is, the extent to which the observations are scattered.
* To use summary statistics to describe collection of data. * To use the mean, median and mode to describe how data “bunch up” * To use the range, variance and standard deviation to describe how data “spread out”.
MEASURES OF CENTRL TENDENCY
Measures of central tendency include three important tools – mean (average), median and mode. Mean
The arithmetic mean is the most common measure of central tendency. For a data set, the mean is the sum of the observations divided by the number of observations. Basically, the mean describes the central location of the data. For a given set of data, where the observations are x1, x2,….,xi ; the Arithmetic Mean is defined as :
The weighted arithmetic mean is used, if one wants to combine average values from samples of the same population with different sample sizes:
Observations| 12| 15| 20| 22| 30|
Weights| 2| 5| 7| 6| 1|
Find the mean.
Observations| Weights| xiwi| Mean =401/21 =19.10|
12| 2| 24| |
15| 5| 75| |
20| 7| 140| |
22| 6| 132| |
30| 1| 30| |
Total| 21| 404| |
* can be specified using and equation, and therefore can be manipulated algebraically * is the most sufficient of the three estimators
* is the most efficient of the three estimators
* is unbiased
* is very sensitive to extreme scores (i.e., low resistance) * value is unlikely to be one of the actual data points
* requires an interval scale
* anything else about the distribution that we’d want to convey to someone if we were describing it to them?
The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one. If there is an even number of observations, the median is not unique, so one often takes the mean of the two middle values. For Odd number of observations:
Median = (n+1)/2 th observations.
For Even number of observations:
Median = Average of (n/2) th and (n/2 + 1) th observations.
Here are the sample test scores you have seen so often:
100, 100, 99, 98, 92, 91, 91, 90, 88, 87, 87, 85, 85, 85, 80, 79, 76, 72, 67, 66, 45 The "middle" score of this group could easily be seen as 87. Why? Exactly half of the scores lie above 87 and half lie below it. Thus, 87 is in the middle of this set of scores. This score is known as the median. In this example, there are 21 scores. The eleventh score in the ordered set is the median score (87), because ten scores are on either side of it. If there were an even number of scores, say 20, the median would fall halfway between the tenth and eleventh scores in the ordered set. We would find it by adding the two scores (the tenth and eleventh scores) together and dividing by two. Advantages
* is unbiased