STAT 271
Business
Statistics
Revision Chapters
1, 2, 3 and 4
Class Activity 1
Required Textbook:
Statistical Techniques
in Business and Economics,
by Douglas A. Lind; William G. Marchal; Samuel A. Wathen:
McGraw-Hill Higher Education, 19th edition.
Required Textbook:
Statistical Techniques
in Business and Economics,
by Douglas A. Lind; William G. Marchal; Samuel A. Wathen:
McGraw-Hill Higher Education, 18th edition.
Required Textbook:
Statistical Techniques
in Business and Economics,
by Douglas A. Lind; William G. Marchal; Samuel A. Wathen:
McGraw-Hill Higher Education, 17th edition.
https://www.academia.edu/
Classify each of the variables listed here as qualitative,
quantitative discrete, quantitative continuous
1.Annual income (pretax dollars)
2.Body temperature (degrees Celsius)
3.Population density (people per acre)
4.Political party affiliation coded
1=Democrat, 2= Republican, 3=Independent, 4=Other
5. Body weight (kg)
6.Grade in a course coded: A, B, C, D, or F
7.Religious identity
8.Blood pressure level classified as either 1=high, 2=normal, 3=low
Classify each of the variables listed here as qualitative,
quantitative discrete, quantitative continuous
9. Satisfaction:
1 =very satisfied, 2 = satisfied, 3 = neutral,
4 = unsatisfied, 5 = very unsatisfied
10.Movie review rating:
1 star, 2 stars, 3 stars, 4 stars, 5 stars
11.Treatment group: 1 = active treatment, 2 = placebo
12.The number of car accidents
13.Nationality
Classify each of the variables listed here as qualitative,
quantitative discrete, quantitative continuous
14.number of family members
15.The order in which runners finish in a race
16.The number of children in a family
17.Car plate numbers
18.IQ level
19.Course credit (pass or fail)
20.Ambient temperature (degrees Fahrenheit)
Classify each of the measurements listed here as nominal,
ordinal, interval or ratio
1.Annual income (pretax dollars)
2.Body temperature (degrees Celsius)
3.Population density (people per acre)
4.Political party affiliation coded
1=Democrat, 2= Republican, 3=Independent, 4=Other
5. Body weight (kg)
6.Grade in a course coded: A, B, C, D, or F
7.Religious identity
8.Blood pressure level classified as either 1=high, 2=normal, 3=low
Classify each of the measurements listed here as nominal,
ordinal, interval or ratio
9. Satisfaction:
1 =very satisfied, 2 = satisfied, 3 = neutral,
4 = unsatisfied, 5 = very unsatisfied
10.Movie review rating:
1 star, 2 stars, 3 stars, 4 stars, 5 stars
11.Treatment group: 1 = active treatment, 2 = placebo
12.The number of car accidents
13.Nationality
Classify each of the measurements listed here as nominal,
ordinal, interval or ratio
14.number of family members
15.The order in which runners finish in a race
16.The number of children in a family
17.Car plate numbers
18.IQ level
19.Course credit (pass or fail)
20.Ambient temperature (degrees Fahrenheit)
Answers
Classify each of the variables listed here as qualitative,
quantitative discrete, quantitative continuous
1. Annual income (pretax dollars) quantitative continuous
2. Body temperature (degrees Celsius) quantitative continuous
3. Population density (people per acre) quantitative continuous
4. Political party affiliation coded
1=Democrat, 2= Republican, 3=Independent, 4=Other qualitative
5. Body weight (kg) quantitative continuous
6. Grade in a course coded: A, B, C, D, or F qualitative
7. Religious identity qualitative
8. Blood pressure level classified as either 1=high, 2=normal, 3=low
qualitative
Classify each of the variables listed here as qualitative,
quantitative discrete, quantitative continuous
9. Satisfaction:
1 =very satisfied, 2 = satisfied, 3 = neutral,
4 = unsatisfied, 5 = very unsatisfied qualitative
10.Movie review rating:
1 star, 2 stars, 3 stars, 4 stars, 5 stars qualitative
11. Treatment group: 1 = active treatment, 2 = placebo qualitative
12. The number of car accidents quantitative discrete
13. Nationality qualitative
Classify each of the variables listed here as qualitative,
quantitative discrete, quantitative continuous
14.number of family members quantitative discrete
15.The order in which runners finish in a race qualitative
16.The number of children in a family quantitative discrete
17.Car plate numbers qualitative
18.IQ level quantitative continuous
19.Course credit (pass or fail) qualitative
20.Ambient temperature (degrees Fahrenheit) quantitative continuous
Classify each of the measurements listed here as nominal,
ordinal, interval or ratio
1. Annual income (pretax dollars) ratio
2. Body temperature (degrees Celsius) interval
3. Population density (people per acre) ratio
4. Political party affiliation coded nominal
1=Democrat, 2= Republican, 3=Independent, 4=Other
5. Body weight (kg) ratio
6. Grade in a course coded: A, B, C, D, or F ordinal
7. Religious identity nominal
8. Blood pressure level classified as either ordinal
1=high, 2=normal, 3=low
Classify each of the measurements listed here as nominal,
ordinal, interval or ratio
9. Satisfaction: ordinal
1 = very satisfied, 2 = satisfied, 3 = neutral,
4 = unsatisfied, 5 = very unsatisfied
10.Movie review rating: ordinal
1 star, 2 stars, 3 stars, 4 stars, 5 stars
11.Treatment group: 1 = active treatment, 2 = placebo nominal
12.The number of car accidents ratio
13.Nationality nominal
Classify each of the measurements listed here as nominal,
ordinal, interval or ratio
14.number of family members ratio
15.The order in which runners finish in a race ordinal
16.The number of children in a family ratio
17.Car plate numbers nominal
18.IQ level interval
19.Course credit (pass or fail) nominal
20.Ambient temperature (degrees Fahrenheit) interval
𝑋 = 1,5,7.5,9 Discrete Variable
2 ≤ 𝑋 ≤ 7 Continous Variable
Ogive
Quantitative(Discrete) Variable
Example (1-3):
The data below represents the number of children in 20
families:
20330422213311542553
Use MegaStat to construct the: Frequency distribution. Bar
Chart
Quantitative(Discrete) Variable
30
Bar Chart
25
Percent
20
15
10
5
0
0
1
2
3
no. of children
4
5
Quantitative(Continuous) Variable
lower limit
upper limit
𝐥𝐨𝐰𝐞𝐫 𝐥𝐢𝐦𝐢𝐭 + 𝐮𝐩𝐩𝐞𝐫 𝐥𝐢𝐦𝐢𝐭
𝐜𝐥𝐚𝐬𝐬 𝐦𝐢𝐝 𝐩𝐨𝐢𝐧𝐭 =
𝟐
Class width = 𝐮𝐩𝐩𝐞𝐫 𝐥𝐢𝐦𝐢𝐭 − 𝐥𝐨𝐰𝐞𝐫 𝐥𝐢𝐦𝐢𝐭
Cumulative Frequency Distribution
Find:
1.
2.
3.
4.
5.
6.
7.
8.
Number of observations
Number of classes
The Width of the class
The lower limit of class 5
The upper limit of class 3
Midpoint of class 2
The frequency of class 4
The percentage of class 4
Classes
Frequency
Cumulative Frequency
20 - 30
30 - 40
2
11-2= 9
2
11
40 - 50
50 - 60
60 - 70
19-11= 8
25-19= 6
37-25= 12
19
25
37
70 - 80
80 - 90
90 - 100
50-37= 13
52-50= 2
54-52= 2
50
52
54
Total
54
Find:
1.
2.
3.
4.
5.
6.
7.
8.
Number of observations = 54
Number of classes = 8
The Width of the class = 10
The lower limit of class 5 = 60
The upper limit of class 3 = 50
Midpoint of class 2 = 35
The frequency of class 4 = 6
The percentage of class 4 = (6/54)×100=11.11%
Mean for Population
σ𝑋
𝜇=
𝑁
Mean for Sample
σ𝑋
𝑋ത =
𝑛
Find the mode of the following data
𝟖, 𝟏𝟓, 𝟕, 𝟑𝟒, 𝟒, 𝟕, 𝟒, 𝟐, 𝟖
𝟖, 𝟏𝟓, 𝟕, 𝟒, 𝟑𝟒, 𝟒, 𝟕, 𝟒, 𝟐, 𝟖
𝟖, 𝟏𝟓, 𝟕, 𝟑, 𝟒, 𝟓, 𝟏, 𝟐, 𝟗
𝟖, 𝟏𝟓, 𝟕, 𝟑, 𝟒, 𝟎, 𝟎, 𝟓, 𝟏, 𝟐, 𝟗
𝟖, 𝟖, 𝟓, 𝟓, 𝟑, 𝟑, 𝟏, 𝟏, 𝟐, 𝟐
Find the mode of the following data
𝟖, 𝟏𝟓, 𝟕, 𝟑𝟒, 𝟒, 𝟕, 𝟒, 𝟐, 𝟖 Mode= 𝟒, 𝟕, 𝟖
𝟖, 𝟏𝟓, 𝟕, 𝟒, 𝟑𝟒, 𝟒, 𝟕, 𝟒, 𝟐, 𝟖
𝟖, 𝟏𝟓, 𝟕, 𝟑, 𝟒, 𝟓, 𝟏, 𝟐, 𝟗
Mode= 𝟒
No Mode
𝟖, 𝟏𝟓, 𝟕, 𝟑, 𝟒, 𝟎, 𝟎, 𝟓, 𝟏, 𝟐, 𝟗 Mode= 0
𝟖, 𝟖, 𝟓, 𝟓, 𝟑, 𝟑, 𝟏, 𝟏, 𝟐, 𝟐
No Mode
There is a unique mean for each data set.
There is a unique median for each data set.
For each data set we can have one mode or
multimode or no mode .
Section A
Section B
10 , 10 , 2 , 1 , 2
5 ,5 ,5 ,5 ,5
𝑋ത = 5
𝑋ത = 5
Section A
Section B
10 , 10 , 2 , 1 , 2
5 ,5 ,5 ,5 ,5
𝑋ത = 5
𝑋ത = 5
𝑅=9
𝑅=0
Data with outliers or extreme values
10 , 10 , 9 , 1
𝑋ത = 7.5
𝑀𝑒𝑑 = 9.5
Data with outliers or extreme values
10 , 10 , 9 , 1
𝑋ത = 7.5
𝑀𝑒𝑑 = 9.5
The median is the best measure of central tendency for
data with outliers or extreme values.
Box-and-Whisker Plot
Box-and-Whisker Plot
Symmetric distribution
Positively (right) skewed distribution
Negatively (left) skewed distribution
What is the shape of the distribution??
What is the shape of the distribution??
The distribution is positively skewed
What is the shape of the distribution??
What is the shape of the distribution??
The distribution is negatively skewed
What is the shape of the distribution??
What is the shape of the distribution??
The distribution is symmetric
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
What is the shape of the distribution?
What is the shape of the distribution?
The distribution is symmetric
Find
1.
2.
3.
4.
5.
6.
7.
8.
Minimum value
Maximum value
Median
Q1
Q3
Range
Mean
Mode
Find
1.
2.
3.
4.
5.
6.
7.
8.
Minimum value = 5
Maximum value = 25
Median =
15
Q1 =
10
Q3 =
20
Range =
25-5 = 20
Mean =
The distribution is symmetric then Mean = Median = Mode=15
Mode =
The distribution is symmetric then Mean = Median = Mode=15
1.
2.
3.
4.
5.
6.
25% of the observation is less than….
50% of the observation is less than….
75% of the observation is less than….
25% of the observation is more than….
50% of the observation is more than….
75% of the observation is more than….
1.
2.
3.
4.
5.
6.
25% of the observation is less than 10
50% of the observation is less than 15
75% of the observation is less than 20
25% of the observation is more than 20
50% of the observation is more than 15
75% of the observation is more than 10
1.The percentage of observations between 5 and 15 is ……
2. The percentage of observations between 10 and 20 is ……
3. The percentage of observations between 10 and 25 is ……
4. The percentage of observations between 5 and 20 is ……
5. The percentage of observations between 5 and 10 is …..
6. The percentage of observations between 5 and 25 is …..
1.The percentage of observations between 5 and 15 is 50%
2. The percentage of observations between 10 and 20 is 50%
3. The percentage of observations between 10 and 25 is 75%
4. The percentage of observations between 5 and 20 is 75%
5. The percentage of observations between 5 and 10 is 25%
6. The percentage of observations between 5 and 25 is 100%