Essay Grade

Running head: DESCRIPTIVE STATISTICS
Descriptive Statistics
Koyel Dutta
Capella University
Copyright © 2016 Capella University. Copy and distribution of this document is prohibited.
1
DESCRIPTIVE STATISTICS
2
Case Study
Mr. Parker owns a casual dining restaurant in Florida. He wants to expand his
business by establishing a chain of family-style restaurants. To make an informed decision,
he assigns Ben to give him a detailed report regarding the various popular family-style
restaurants in the city. He collects the required data online and consolidates it into a
Restaurant Data file. This file is e-mailed to Ben with the instruction that he should analyze
the data and come up with recommendations about the most important aspects of establishing
a successful family-style restaurant chain, the data is provided (see Appendix A, Table A1 for
more information on the Restaurant Data). The Restaurant Data file contains the data of 50
major family-style restaurants including the price of food of various family-style restaurants,
the number of people who visit the restaurants per day, the seating capacity of the restaurants,
and the average rating given by the customers per day. The seating capacity of a restaurant is
the number of people who can be seated in a specific space, in terms of the physical space
available. The ratings are given on a scale of 1 to 5, 1 being the lowest.
Mean, Median, Range, Standard Deviation, and Mode
The mean is the average of the data that is computed by dividing the sum of the
observations by the total number of observations. To find the median, rewrite the list of
numbers in numerical order and the middlemost value of the ordered data is the median. The
mode is the value of the number that occurs with the maximum frequency in the list. If no
number is repeated, then there is no mode for the list. The range is the difference between the
largest and smallest values in the list.
The standard deviation is a measure of dispersion; it shows how widely spread the
numbers are. The standard deviation can be computed by taking the square root of the
Copyright © 2016 Capella University. Copy and distribution of this document is prohibited.
Comment [JK1]: Very good with the
overview of the problem…
Comment [JK2]: Okay with the definition
the measures. Though they are not needed
for the reporting. You only have to apply th
concepts
DESCRIPTIVE STATISTICS
3
variance. The variance is nothing but the average of the squared differences from the mean. If
the data points are further from the mean, the deviation is high within the data set
N
2
The Population Standard Deviation:   1 N  ( xi   )  .
 i 1

N
2
The Sample Standard Deviation: s  1 N  1  ( xi  x)  .
 i 1

Comment [JK3]: These are so standard yo
do not need any citation for them
(Coolican, 2014).
The calculated values of mean, median, range, and standard deviation of price of food per
couple in the major family-style restaurants in Florida and the number of people visiting the
restaurants are shown in Table 1.
Table 1
Mean, Median, Range, Standard Deviation, and Mode Results
Restaurant data
Mean
Median
Range
Standard
deviation
Mode
(in $)
Number of
people who
visit the
restaurant
(per day)
97.8
97.0
114
111
121 .0
146
31.1
37
Price of
food (per
couple)
Seating
capacity
125
The mean here gives us an idea about the average price and the number of people
visiting the major family-style restaurants in Florida. Table 1 shows an average of 114 people
visit a restaurant where the average cost of food per couple is $97.8. The median here is the
Copyright © 2016 Capella University. Copy and distribution of this document is prohibited.
Comment [JK4]: Good with the evaluation
of the descriptive summaries.
DESCRIPTIVE STATISTICS
4
middle most value of the price of food per couple and the number of people visiting the
restaurant per day. Here, the median for the price of food is $97 and the median for the
number of people who visit the restaurant per day is 111. The mode depicts that the majority
of the restaurants in the data have a seating capacity of 125.
Histogram
From the Restaurant Data, a histogram has been created to show the number of
restaurants by price range, in increments of $20. Table 2 shows interval and frequency based
Comment [JK5]: Should be Frequency
distribution of the price of food per couple.
on the given data.
Table 2
Comment [JK6]: This chart should be on t
“Distribution of Price of Food”
Frequency Distribution of the Restaurant Data
Lower
Upper
Frequency
$19.5
$39.5
3
$39.5
$59.5
1
$59.5
$79.5
12
$79.5
$99.5
11
$99.5
$119.5
8
$119.5
$139.5
10
$139.5
$159.5
5
Copyright © 2016 Capella University. Copy and distribution of this document is prohibited.
DESCRIPTIVE STATISTICS
5
Figure 1
Restaurant Food Price Range Histogram
Restaurant Food Price Range Histogram
14
Frequency
12
Comment [JK7]: Okay with the creation o
the histogram. Could improve with the
presentation. The width notation should
reflect the intervals. That is 19.5 -39, 39-5-5
etc., etc.
You are using the lower value, but is it not
well presented on the chart. As presented,
is looks more like the midpoint which would
not be accurate.
10
8
6
If the intend is using the midpoint to
represent the interval width indicate the
correct values. If you want to use lower valu
place them at the beginning of the width, no
the middle.
4
2
0
Price of Food (per couple)
Figure 1 displays that the frequency of the restaurants is maximum between the price range of
$59.5 and $79.5 followed by the price range $79.5 and $99.5. As shown in Figure 1 the
number of restaurants in the range of $39.5 and $59.5 is the least. It is evident that there are
many restaurant options available in the price range of $59.5 and $99.5.
Comment [JK8]: This is not apparent from
the chart.
See comments above.
Table 1 gives a better presentation.
Scatter plot
A scatter plot is a graphic tool that displays the relationship between two quantitative
variables. A graph of plotted points shows the relationship between the two sets of data.
Figure 2 is a scatterplot that establishes the relation between the seating capacity of and the
number of people visiting the restaurants per day.
Copyright © 2016 Capella University. Copy and distribution of this document is prohibited.
DESCRIPTIVE STATISTICS
6
Figure 2
Scatter Plot Showing the Relationship between the Seating Capacity of and the Number of
People Visiting the Restaurants
Seating Capacity
The Number of People Visiting the Restaurants and the
Seating Capacity
Comment [JK9]: Good with the creation o
the scatter plot.
200
150
100
50
0
0
50
100
150
200
250
Number of People Visiting the Restaurants (per day)
Figure 2 indicates a positive relationship between the seating capacity of and the number of
people visiting the restaurants. The number of people visiting is comparatively more in
restaurants which have more seating capacity. This scatter plot gives an idea about the
number of people to be expected to visit the restaurants based on the seating capacity
provided by the major family-style restaurants in Florida.
Recommendation
From the analysis of the results obtained so far, it can be said that the average price of
food per couple in the major family-style restaurants is $97.8. Moreover, as Mr. Parker wants
to open a chain of family-style restaurants in Florida, it is advisable that he opts for
restaurants in the price range of $39.5 to $59.5, as the number of restaurants is limited in this
price range. Most restaurants have a seating capacity of 125, so it is advisable that Mr. Parker
keeps the seating capacity of his restaurant at 125 or above. The scatter plot shows that the
number of people visiting a restaurant will increase with the seating capacity of the
Copyright © 2016 Capella University. Copy and distribution of this document is prohibited.
Comment [JK10]: Very good with the
description of the relationship between
seating capacity and number of people
visiting.
DESCRIPTIVE STATISTICS
7
restaurant. On an average, 114 people visit the major family-style restaurants daily. Hence, if
he wants more than 114 people to visit his restaurant per day, the restaurant must have a
seating capacity of more than 125. Also, the scatter plot makes it evident that the number of
restaurants is clustered around a certain price range. From the analysis, it is evident that there
are 22 family-style restaurants in Florida with a seating capacity of more than 100 and a
rating above 3. But there are only four family-style restaurants where the price of food per
couple is less than $59.5 and the seating capacity is less than 100. Thus, it would be a
convenient choice for Mr. Parker to keep the price of food per couple in his restaurant under
$59.5. This would help him get good ratings and attract more customers provided that he
maintains the quality of food and service in his chain of restaurants.
Conclusion
The various measures of central tendency mentioned above provide an insight about
the data. It will help Mr. Parker understand the relationship between the seating capacity of
and the number of people visiting the restaurants in Florida. The histogram also shows the
distribution of the restaurants according to the price range. It will help Mr. Parker to make an
informed decision on creating his own chain of family-style restaurants in Florida.
Copyright © 2016 Capella University. Copy and distribution of this document is prohibited.
DESCRIPTIVE STATISTICS
8
References
Coolican, H. (2014). Research methods and statistics in psychology. Retrieved from
http://ebookcentral.proquest.com.library.capella.edu/lib/capella/reader.action?docID=
1664258.
Copyright © 2016 Capella University. Copy and distribution of this document is prohibited.
Comment [JK11]: The reference here is n
needed because it was referencing standard
foundational information. See comments in
text
DESCRIPTIVE STATISTICS
9
Appendix A
Restaurant Data
Mr. Parker owns a casual dining restaurant in Florida. Now, he wants to establish a chain of
family-style restaurants. He assigns Ben to give him a detailed report regarding the various
popular family-style restaurants in the city. He e-mails Ben the Restaurant Data file and asks
him to find ways to use data to describe the most important aspects for creating the food
chain. The Restaurant Data file contains the data of 50 major family-style restaurants
including the food price of various family-style restaurants, the number of people who visit
the restaurants per day, the seating capacity of the restaurants, and the average rating given
by the customers per day.
Table A1
The Restaurant Data
Restaurant data
Restaurant
Price of food
(per couple) (in
$)
1
2
3
4
5
6
7
8
9
10
11
12
13
144
97
130
80
110
124
91
35
128
112
122
61
38
Number of
people who
visit the
restaurant (per
day)
170
73
85
75
118
175
182
78
64
94
148
109
79
Average rating
by the
customer (per
day)
Seating
capacity
4
2
2
1
4
5
5
3
2
3
4
5
2
110
60
72
68
100
130
150
85
60
85
115
128
65
Copyright © 2016 Capella University. Copy and distribution of this document is prohibited.
DESCRIPTIVE STATISTICS
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
138
112
75
128
33
67
75
126
131
67
75
102
82
67
78
92
130
142
90
150
97
123
115
98
76
81
68
108
73
154
116
54
64
148
93
85
107
10
163
175
200
60
81
109
55
112
134
85
108
136
128
54
124
105
138
85
115
197
125
75
152
102
125
138
115
142
95
133
69
85
105
98
146
120
80
5
5
5
2
3
4
1
3
5
3
5
5
5
1
4
3
3
2
4
3
5
3
4
5
4
4
2
4
2
5
1
2
5
5
4
5
1
125
168
190
50
85
125
60
85
125
72
100
112
150
60
105
85
125
72
125
180
92
60
130
125
155
100
92
112
62
102
55
70
125
102
130
92
72
Copyright © 2016 Capella University. Copy and distribution of this document is prohibited.
Florida Pool Home Data
Home
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
Price
($1000s)
260.9
337.3
268.4
242.2
255.2
205.7
249.5
193.6
242.7
244.5
184.2
325.7
266.1
166.0
330.7
289.1
268.8
276.7
222.4
241.5
307.9
223.5
231.1
216.5
205.5
258.3
227.6
255.4
235.7
285.1
284.8
193.7
247.5
274.8
264.4
204.1
273.9
238.5
274.4
259.6
285.6
216.1
261.3
Size (Square
Feet)
2666
3418
2945
2942
2798
2210
2209
2465
2955
2722
2590
3138
2713
2284
3140
3205
2721
3245
2464
2993
2647
2670
2895
2643
2915
2800
2557
2805
2878
2795
2748
2256
2659
3241
3166
2466
2945
2727
3141
2552
2761
2880
3426
Number of
Bathrooms
2.5
3.5
2.0
2.5
3.0
2.5
2.0
2.5
2.0
2.5
2.5
3.5
2.0
2.5
3.5
2.5
2.5
2.5
3.0
2.5
3.5
2.5
2.5
2.5
2.0
3.5
2.5
2.0
2.5
3.0
2.5
2.5
2.5
3.5
3.0
2.0
2.5
3.0
4.0
2.0
3.0
2.5
3.0
Niceness
Rating
7
6
5
3
3
2
7
1
4
5
1
7
7
2
6
3
5
2
3
1
6
4
3
3
1
2
3
3
4
7
7
2
2
4
3
4
5
1
4
7
6
2
1
Pool? (yes=1;
no=0)
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
End of worksheet
236.4
267.5
220.2
300.1
260.0
277.5
274.9
259.8
235.0
191.4
228.5
266.6
233.0
343.4
334.0
289.7
228.4
233.4
275.7
290.8
230.8
310.1
247.9
249.9
220.5
226.2
313.7
210.1
244.9
235.8
263.2
280.2
290.8
235.4
190.3
234.4
238.7
2895
2726
2930
3013
2675
2874
2765
3020
2887
2032
2698
2847
2639
3431
3485
2991
2482
2712
3103
3124
2906
3398
3028
2761
2842
2666
2744
2508
2480
2986
2753
2522
2808
2616
2603
2804
2851
2.5
3.0
2.5
2.5
2.0
3.5
2.5
3.5
2.5
2.0
2.5
3.0
3.0
4.0
3.5
2.5
2.5
2.5
2.5
2.5
2.5
4.0
3.0
2.0
3.0
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2
7
2
6
6
4
2
2
1
3
4
2
3
5
5
6
2
1
2
3
2
4
4
5
3
6
7
4
5
4
7
6
7
3
2
4
5
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0

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