Graphing Grouped Data
Monday, September 02, 2019 1:22 PM
Single-Valued Classes
Question:
The administration in a large city wanted to know the distribution of the number of
vehicles owned by households in that city. A sample of 40 randomly selected
households from this city produced the following data on the number of vehicles
owned.
Construct a frequency distribution table for these data using single-valued classes.
Frequency Distribution of the Number of Vehicles Owned
Vehicles Number
Owned of Households ( f)
0
1
2
3
4
5
∑f=
Vehicles Number
Owned of Households ( f)
0 2
1 18
2 11
3 4
4 3
5 2
∑f=40
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Dot Plot:
One of the simplest graphical summaries of data is a dot plot. A horizontal axis shows the range for
the data. Each data value is represented by a dot placed above the axis.
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Shapes of Histograms
A histogram can assume any one of a large number of shapes. The most common of
these shapes are
• Symmetric
• Skewed
• Uniform or rectangular
A symmetric histogram is identical on both sides of its central point. The histograms
shown in Figure below are symmetric around the dashed lines that represent their
central points.
A skewed histogram is nonsymmetric. For a skewed histogram, the tail on one side is
longer than the tail on the other side. A skewed-to-the-right histogram has a longer
tail on the right side. A skewed-to-the-left histogram has a longer tail on the left
side.
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.
Cumulative Frequency Distributions
Example:
The following data give the total number of Nokia phones sold by a Daraz on each of 30 days.
Construct a frequency distribution table.
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
Phones sold Class Boundaries Frequency Cumulative Frequency
5-9 4.5-9.5 3 3
5-14 4.5-14.5 6 3+6=9
5-19 4.5-19.5 8 9+8=17
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5-19 4.5-19.5 8 9+8=17
5-24 4.5-24.5 8 17+8=25
5-29 4.5-29.5 5 25+5=30
Sum=30 Sum=30
19 or fewer Phones were sold on 17 days.
Phones sold Frequency Cumulative Frequency Cumulative
Relative Frequency
5-9 3 3 3/30
5-14 6 3+6=9
5-19 8 9+8=17
5-24 8 17+8=25
5-29 5 25+5=30
Sum=30 Sum=30
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Question :
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Scatter Diagram and Trendline
Incomes and Food Expenditures of Seven Households
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a trendline is a line that provides an approximation of the relationship
TYPES OF RELATIONSHIPS DEPICTED BY SCATTER DIAGRAMS
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TYPES OF RELATIONSHIPS DEPICTED BY SCATTER DIAGRAMS
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Exploratory Data Analysis:
Monday, September 02, 2019 3:26 PM
The techniques of exploratory data analysis consist of simple arithmetic and easy-to-
draw graphs that can be used to summarize data quickly
Stem-and-Leaf Displays:
5
6
7
8
9
Advantages:
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Wrong Representations
Cross tabulations and Scatter Diagrams
Cross tabulation is a tool that allows you compare the relationship between
two variables.
QUALITY RATING AND MEAL PRICE FOR 300 RESTAURANTS
Restaurants Quality Rating Meal Price
1 Good 18
2 Very Good 22
3 Excellent 28
4 Good 38
5 Good 18
6 Very Good 22
7 Excellent 28
8
Relative and percent frequency distribution
Quality Rating Relative Frequency Percent Frequency
Good .28 28
Very Good .50 50
Excellent .22 22
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CROSSTABULATION OF QUALITY RATING AND MEAL PRICE FOR 300 RESTAURANTS
Meal Price/Quality Rating 10-19 20- 29 30-39 40-49 Total
Good 42 40 2 0 84
Very Good 34 64 46 6 150
Excellent 2 14 28 22 66
Total 78 118 76 28 300
Relative and percent frequency distribution for the meal price
Meal Price Relative frequency Percent Frequency
10-19
20-29
30-39
40-49
Total
ROW PERCENTAGES FOR EACH QUALITY RATING CATEGORY
Meal Price/Quality Rating 10-19 20-29 30-39 40-49 Total
Good
Very Good
Excellent
Question:
Recently, management at Oak Tree Golf Course received a few complaints about the condition of the
greens. Several players complained that the greens are too fast. Rather than react to the comments of
just a few, the Golf Association conducted a survey of 100 male and 100 female golfers. The survey
results are summarized here.
a. Combine these two crosstabulations into one with Male and Female as the row
labels and Too Fast and Fine as the column labels. Which group shows the highest
percentage saying that the greens are too fast?
b. Refer to the initial crosstabulations. For those players with low handicaps (better
players), which group (male or female) shows the highest percentage saying the
greens are too fast?
c. Refer to the initial crosstabulations. For those players with higher handicaps, which
group (male or female) shows the highest percentage saying the greens are too
fast?
d. What conclusions can you draw about the preferences of men and women
concerning the speed of the greens? Are the conclusions you draw from part (a) as
compared with parts (b) and (c) consistent? Explain any apparent inconsistencies.
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a.
Gender/ Conditions Male Female
Too Fast
Fine
b.
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Review
Monday, September 02, 2019 5:04 PM
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