Statistics: Descriptive Statistics and Data Analysis, Schemes and Mind Maps of Industrial Engineering

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Computer

Applications in IE

Introduction to Descriptive

Statistics

Assoc. Prof. Ho Thanh Phong HCMC University of Technology

Contents

OUTLINES

• Introduction to Descriptive Statistics
• Sample and Population
• Grouped Data and the Histogram
• Percentiles and Quartiles
• Measures of Central Tendency
• Measures of Variability
• Mean and Standard Deviation
• Data displaying
• Exploratory Data Analysis

Samples and Populations

X , s , pˆ

2 Dept. of Industrial & Systems Engineering 4

A population consists of the set of all measurements in which the investigator is

interested.

A sample is a subset of the measurements selected from the population.

A census is a complete enumeration of every item in a population.

Population (N)

Sample (n)

, , p 2

Why Sample? Census of a population may be: Impossible, Impractical, too costly To estimate the population parameters

Sampling

Estimation

THUẬT NGỮ

Descriptive Statistics: thống kê mô tả

Inferential Statistics: thống kê suy luận

Population: quần thể

Sample: mẫu

Census: điều tra tổng thể

Two Types of Data

Qualitative (Categorical,

Nominal or Non-metric):

Examples:

❑ Color

❑ Gender

❑ Nationality

Quantitative ( Measurable,

Countable or Metric):

Examples:

❑ Temperatures

❑ Salaries

❑ Number of points scored

on a 100-point exam

Scales of Measurement

Nominal Scale - groups or classes

❑ Gender

Ordinal Scale - order matters

❑ Ranks

Interval Scale - difference or distance matters

❑ Temperatures

Ratio Scale - Ratio matters

❑ Salaries

Group Data and the Histogram

Dividing data into groups or classes or intervals

Groups should be:

Mutually exclusive

❑ Not overlapping - every observation is assigned to only

one group

Exhaustive

❑ Every observation is assigned to a group

Equal-width (if possible)

❑ First or last group may be open-ended

Frequency Distribution

Class midpoint is the middle value of a group or class or

interval

❑ Relative frequency is the percentage of total

observations in each class

▪ Sum of relative frequencies = 1

❑ Cumulative frequency: a running total of frequencies

through the classes

Example

Class Midpoint Frequency Relative Cumulative Cumulative Frequency Frequency Relative Fre. 1 to less than 3 2 16 0.40 16 0. 3 to less than 5 4 2 0.05 18 0. 5 to less than 7 6 4 0.10 22 0. 7 to less than 9 8 3 0.075 25 0. 9 to less than 11 10 9 0.225 34 0. 11 to less than 13 12 6 0.150 40 1. Total 40 1.

Histogram

Dept. of Industrial & Systems Engineering 14

A histogram is a chart made of bars of different heights.

❑ Widths and locations of bars correspond to widths and locations

of data groupings

❑ Heights of bars correspond to frequencies or relative frequencies

of data groupings

4. 0
5. 0
6. 0
7. 0 0 F re q u e n c y Numbers

2 4 6 8 10 12

THUẬT NGỮ

Histogram: biểu đồ cột

Percentiles: bách phân vị

An ascending array : dãy tăng dần

Whole number: số nguyên

Examples

A large department store collects data on sales made by each of its salespeople. The

number of sales made on a given day by each of 20 salespeople is shown. Also, the data

has been sorted in magnitude. n = 22

Sales 9 6 12 10 13 15 16 14 14 16 17 16 24 21 22 18 19 18 20 17 27 29 Sorted Sales 6 9 10 12 13 14 14 15 16 16 16 17 17 18 18 19 20 21 22 24 27 29 Order 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Find the 50

th

th

, and the 90

th

percentiles of this data set.

❑ To find the 50 th percentile, determine the data point in position nP/ 100 = ( 22 )( 50 / 100 ) = 11 is a whole number. The 50 th percentile is the average value of the 11 th values and the 12 th value: 16. 5. ❑ To find the 80 th percentile, the location is nP/ 100 = ( 22 )( 80 / 100 ) = 17. 6 is not a whole number. The 80 th percentile is the value of the 18 th values: 21 ❑ To find the 90 th percentile, the location is nP/ 100 = ( 22 )( 90 / 100 ) = 19. 8 The 90 th percentile is the value of the 20 th values: 24

Interquartile Range

❑ The first quartile (25th percentile) is often called the

lower quartile.

❑ The second quartile (50th percentile) is often called

median or the middle quartile.

❑ The third quartile (75th percentile) is often called the

upper quartile.

❑ The interquartile range is the difference between the first

and the third quartiles.

THUẬT NGỮ

Quartiles: tứ phân vị

Median: trung vị

Interquartile Range: khoảng liên tứ phân