Business Statistics **** Management Information Systems Business Statistics Third level First mid-term: Instructor: Dr. ZRELLI Houyem Majmaah University ***** Faculty of Science and Humanities in Ghat

Third level Majmaah University Dr: ZRELLI Houyem 1 Chapter 2; Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation Business Statistics **** Management Information Systems

Data Presentation Qualitative Data Quantitative Data Continues Variables Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 2 Discrete Variables

Qualitative Data are nonnumerical – Major Discipline – Political Party – Gender – Eye color Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 3  Describing Qualitative Data

Summarized in two ways: – Class Frequency – Class Relative Frequency Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 4  Describing Qualitative Data

Class Frequency – A class is one of the categories into which qualitative data can be classified – Class frequency is the number of observations in the data set that fall into a particular class Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 5  Describing Qualitative Data

StudentEvaluationStudentEvaluation 1Very Good12Very Good 2Good13Good 3 14Very Good 4Excellent15Good 5Very Good16Good 6Excellent17Good 7Excellent18Excellent 8Good19Very Good 9Excellent20Good 10Good21Good 11Excellent22Excellent Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 6  Describing Qualitative Data Example: Student evaluations

EvaluationFrequency Good10 Very Good5 Excellent7 Total22 Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 7  Describing Qualitative Data Example: Student evaluations

Class Relative Frequency – Class frequency divided by the total number of observations in the data set Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 8  Describing Qualitative Data

Class Percentage – Class relative frequency multiplied by 100 Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 9  Describing Qualitative Data

EvaluationRelative Frequency Class Percentage Good10/22 = % Very Good5/22 = % Excellent7/22 = % Total22/22 = % Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 10  Describing Qualitative Data Example: Student evaluations

Bar Graph: The categories (classes) of the qualitative variable are represented by bars, where the height of each bar is either the class frequency, class relative frequency or class percentage. Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 11  Describing Qualitative Data Example: Student evaluations

Pie Chart: The categories (classes) of the qualitative variable are represented by slices of a pie. The size of each slice is proportional to the class relative frequency. Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 12  Describing Qualitative Data Example: Student evaluations

Pareto Diagram: A bar graph with the categories (classes) of the qualitative variable (i.e., the bars) arranged in height in descending order from left to right. Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 13  Describing Qualitative Data Example: Student evaluations

 Quantitative data: Discrete Variable Third level Majmaah University Dr: ZRELLI Houyem 14 A discrete variable can have only countable number of values Examples: Family size (x = 0, 1, 2, 3, … ) Number of patients (x = 0, 1, 2, 3, … ) Business Statistics **** Management Information Systems

Example: The following data represent the number of children of 16 Saudi women: 3, 5, 2, 4, 0, 1, 3, 5, 2, 3, 2, 3, 3, 2, 4, 1 - Variable = X = no. of children (discrete, quantitative) - Sample size = n = 16 - The possible values of the variable are: 0, 1, 2, 3, 4, 5  Quantitative data: Discrete Variable Third level Majmaah University Dr: ZRELLI Houyem 15 Business Statistics **** Management Information Systems

no. of children (variable) Frequency (no. of women) Relative Freq. (R.F.) (=Freq /n) Percentage Freq. (= R.F. * 100%) % % % % % % Total n= % Note Total of the frequencies = n = e sample size · Relative frequency = frequency/n Percentage frequency = Relative frequency *100% Simple frequency distribution of the no. of children Third level Majmaah University Dr: ZRELLI Houyem 16 Business Statistics **** Management Information Systems  Quantitative data: Discrete Variable

The most common form of graphs for discrete variables is the bar chart. Third level Majmaah University Dr: ZRELLI Houyem 17 Business Statistics **** Management Information Systems  Graphical representation of discrete variables

· Frequency bar chart Third level Majmaah University Dr: ZRELLI Houyem 18 Business Statistics **** Management Information Systems  Graphical representation of discrete variables

Third level Majmaah University Dr: ZRELLI Houyem 18 Business Statistics **** Management Information Systems  Cumulative representation of discrete variables No. Of children Frequency Relative frequency Cumulative relative frequency TotalN=

Third level Majmaah University Dr: ZRELLI Houyem 18 Business Statistics **** Management Information Systems  Cumulative representation of discrete variables modalities FiFi Cumulative distribution

A continuous variable can have any value within a certain interval of values.  Quantitative data: Continuous variables Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 19 Examples: - height (140 < x < 190) - blood sugar level (10 < x < 15)

A continuous frequency distribution CANNOT be represented by a bar chart. It is most appropriately represented by a histogram Third level Majmaah University Dr: ZRELLI Houyem 20 Business Statistics **** Management Information Systems  Graphical representation of continuous variables

Example: Hudson Auto Repair The manager of Hudson Auto would like to have a better understanding of the cost of parts used in the engine tune-ups performed in the shop. She examines 50 customer invoices for tune-ups. The costs of parts, rounded to the nearest dollar, are listed on the next slide. Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 21

Example: Hudson Auto Repair n Sample of Parts Cost for 50 Tune-ups Including a line in the table for every possible cost is not a good idea. Need to categorize. Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 22

Frequency Distribution Guidelines for Selecting Number of Classes Use between 5 and 20 classes. Use between 5 and 20 classes. Data sets with a larger number of elements Data sets with a larger number of elements usually require a larger number of classes. usually require a larger number of classes. Smaller data sets usually require fewer classes Smaller data sets usually require fewer classes Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 23

Frequency Distribution Guidelines for Selecting Width of Classes Use classes of equal width. Use classes of equal width. Approximate Class Width = Approximate Class Width = Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 24

Frequency Distribution For Hudson Auto Repair, if we choose six classes: [50-60[ [60-70[ [70-80[ [80-90[ [90-100[ [ [ Total 50 Parts Cost ($) Frequency Approximate Class Width = ( )/6 = 9.5  10 Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 25

Relative Frequency and Percent Frequency Distributions [50-60[ [50-60[ [60-70[ [60-70[ [70-80[ [70-80[ [80-90[ [80-90[ [90-100[ [90-100[ [ [ [ [ Parts Cost ($) Total 1.00 Relative RelativeFrequency Percent Frequency Frequency 2/502/50.04(100).04(100) Preview cumulative frequencies here. Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 26

Only 4% of the parts costs are in the $50-60 class. Only 4% of the parts costs are in the $50-60 class. The greatest percentage (32% or almost one-third) The greatest percentage (32% or almost one-third) of the parts costs are in the $70-80 class. of the parts costs are in the $70-80 class. 30% of the parts costs are under $70. 30% of the parts costs are under $70. 10% of the parts costs are $100 or more. 10% of the parts costs are $100 or more. n Insights Gained from the Percent Frequency Distribution Relative Frequency and Percent Frequency Distributions Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 27

Histogram Another common graphical presentation of quantitative Another common graphical presentation of quantitative data is a histogram. data is a histogram. The variable of interest is placed on the horizontal The variable of interest is placed on the horizontal axis. axis. A rectangle is drawn above each class interval with A rectangle is drawn above each class interval with its height corresponding to the interval’s frequency, its height corresponding to the interval’s frequency, relative frequency, or percent frequency. relative frequency, or percent frequency. Unlike a bar graph, a histogram has no natural Unlike a bar graph, a histogram has no natural separation between rectangles of adjacent classes. separation between rectangles of adjacent classes. In informal discussions bar graphs and histograms are often equated. In this class you should be careful to keep them straight. Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 28

Histogram Parts Cost ($) Parts Cost ($) Frequency  Tune-up Parts Cost Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 29

Symmetric – Left tail is the mirror image of the right tail – Examples: heights and weights of people Histogram (Common categories) Relative Frequency Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 30

Cumulative frequency distribution  shows the Cumulative frequency distribution  shows the number of items with values less than or equal to number of items with values less than or equal to the upper limit of each class.. the upper limit of each class.. Cumulative frequency distribution  shows the Cumulative frequency distribution  shows the number of items with values less than or equal to number of items with values less than or equal to the upper limit of each class.. the upper limit of each class.. Cumulative relative frequency distribution – shows Cumulative relative frequency distribution – shows the proportion of items with values less than or the proportion of items with values less than or equal to the upper limit of each class. equal to the upper limit of each class. Cumulative relative frequency distribution – shows Cumulative relative frequency distribution – shows the proportion of items with values less than or the proportion of items with values less than or equal to the upper limit of each class. equal to the upper limit of each class. Cumulative Distributions Cumulative percent frequency distribution – shows Cumulative percent frequency distribution – shows the percentage of items with values less than or the percentage of items with values less than or equal to the upper limit of each class. equal to the upper limit of each class. Cumulative percent frequency distribution – shows Cumulative percent frequency distribution – shows the percentage of items with values less than or the percentage of items with values less than or equal to the upper limit of each class. equal to the upper limit of each class. Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 31

Cumulative Distributions Hudson Auto Repair [50-60[ [60-70[ [70-80[ [80-90[ [90-100[ [ [ Cost ($) Cumulative CumulativeFrequency RelativeFrequency CumulativePercent Frequency Frequency /5015/50.30(100).30(100) Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 32

Ogive n An ogive is a graph of a cumulative distribution. n The data values are shown on the horizontal axis. n Shown on the vertical axis are the: cumulative frequencies, or cumulative frequencies, or cumulative relative frequencies, or cumulative relative frequencies, or cumulative percent frequencies cumulative percent frequencies n The frequency (one of the above) of each class is plotted as a point. n The plotted points are connected by straight lines. Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 33

Parts Parts Cost ($) Parts Parts Cost ($) Cumulative Percent Frequency (89.5, 76) Ogive with Cumulative Percent Frequencies Tune-up Parts Cost Business Statistics **** Management Information Systems Third level Majmaah University Dr: ZRELLI Houyem 34

End of Chapter 2