Session 7, 8

CRT 1006BUSINESS STATISTICS

Review• Frequency Distribution– Considers one variable at a time– Produces a table of frequency counts, percentages and

cumulative percentages for all values associated with that variable

• Statistics associated with F.D.– Measures of Location• Measures of central tendency – mean, median, mode

– Measures of variability – range, interquartile range, standard deviation, variance

– Measures of shape • Skewness• Kurtosis

• Examples of Univariate – How many users of the brand may be characterized as brand-

loyal?– What percentage of the market consists of heavy users,

medium users, light users and non-users?• Examples of Bivariate – How many brand-loyal users are male?– Is product use (measured in terms of heavy users, medium

users, light users and nonusers) related to interest in outdoor activities (high, medium and low)?

Frequency Distribution

Univariate, Bivariate and Multivariate Distributions

• Univariate – Distributions involving only one variable

• Bivariate– Distributions involving two variables

• Multivariate– Distributions involving more than two variables

Bivariate Distribution & Correlation Analysis

• Two variables– Known variable – independent variable– Variable we are trying to predict – dependent variable

• Correlation– Statistical tool which studies the relationship between

two variables– Two variables are said to be correlated if the change in

one variable results in a corresponding change in the other variable

Types of correlation

• Positive and negative correlation• Linear and non-linear correlation Correlation and Causation• Gives an idea about the degree and direction of

relationship between the two variables• Fails to reflect on the causation

Studying correlation

1. Scatter Diagram method2. Karl Pearson’s coefficient of correlation

S 4 Q1An instructor is interested in finding out how the number of students

absent on a given day is related to the mean temperature that day. A random sample of 10 days was used for the study. The following data indicate the number of students absent and the mean temperature for each day.

a) State the dependent variable (Y) and the independent variable (X)b) Draw a scatter diagram of the datac) Does the relationship appear to be linear or curvilinear? d) How can you explain the diagram?e) Repeat the exercise using SPSS to draw the scatter diagram

ABS 8 7 5 4 2 3 5 6 8 9

TEMP 10 20 25 30 40 45 50 55 59 60

S4 Q2 A professor is trying to show his students the importance of quizzes even though 90%

of the final grade is determined by exams. He believes that the higher the quiz grade, the higher the final grade. A random sample of 15 students in his class was selected with the data given below:

a) State the dependent variable (Y) and the independent variable (X)b) Draw a scatter diagram of these datac) Does the professor’s belief appear to be justified? Explain your reasoning. d) Repeat using SPSS.

Quiz Average

59 92 72 90 95 87 89 77 76 65 97 42 94 62 91

Final average

65 84 77 80 77 81 80 84 80 69 83 40 78 65 90