Bài giảng nguyên lý thông kê chương 3 numerical measures part b student

Chapter 3Statistical measures Measure center and location Measure variation/dispersion... Statistical measures Center and location Variation/ Dispersion - Coefficient of variation... T

Chapter 3

Statistical measures

Measure center and location

Measure

variation/dispersion

Statistical measures

Center and

location

Variation/ Dispersion

- Coefficient of variation

Part B Measures of variation/dispersion

1 The range

 The range is defined as the numerical difference between the smallest and largest values of the items in a set or distribution

 Formula:

R = largest value – smallest

value

Advantages and disadvantages

of the range

 Advantages:

 Disadvantages:

Implication

2 The mean deviation

dispersion that gives the average

difference (i.e ignoring ‘-’ signs) between each item and mean.

f x x d

x x d

x x d

person)

Number

of workers

Characteristics of the mean

 Can be complicated to calculate in

practice if the mean is anything

other than a whole number

3 Variance

 Variance is another statistical

measure of dispersion

 It is defined as the average of

squared discrepancies between each data value and their mean

 Formula:

For a set of values

i i

x x n

 







person)

Number

of workers

4 Standard deviation

 Standard deviation is defined as the square root of the variance

 Formula

For a set of values

i i

person)

Number

of workers

Characteristics of Standard

Deviation

 Can be regarded as one of the most useful and appropriate measure of dispersion.

 For distribution that are not too skewed:

- 99.7% of the data items should lie within three standard deviation of the mean

- 95% of the data items should lie within

two standard deviation

- 68% of the data items should lie within

one standard deviation of the mean

 Over a period of three months, the daily number of components

produced by two comparable

machines was measured, giving the following statistics: