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Running head: DESCRIPTIVE STATISTICS 1

Descriptive Statistics

Koyel Dutta

Capella University

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

Comment [JK1]: Very good with the overview of the problem…

Comment [JK2]: Okay with the definition of the measures. Though they are not needed for the reporting. You only have to apply the 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

(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

Price of

food (per

couple)

Number of

people who

visit the

restaurant

Seating

capacity

(in $) (per day)

Mean 97.8 114

Median 97.0 111

Range 121 .0 146 Standard

deviation 31.1 37

Mode 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

The Population Standard Deviation: 2

1 ( ) N

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   .

The Sample Standard Deviation: 2

1 1 ( ) N

s N x x 

     

   .

Comment [JK3]: These are so standard you do not need any citation for them

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

on the given data.

Table 2

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

Comment [JK5]: Should be Frequency distribution of the price of food per couple.

Comment [JK6]: This chart should be on the “Distribution of Price of Food”

DESCRIPTIVE STATISTICS 5

Figure 1

Restaurant Food Price Range Histogram

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.

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.

F r e q

u e n

c y

Price of Food (per couple)

Restaurant Food Price Range Histogram

Comment [JK7]: Okay with the creation of the histogram. Could improve with the presentation. The width notation should reflect the intervals. That is 19.5 -39, 39-5-59, etc., etc. You are using the lower value, but is it not well presented on the chart. As presented, it is looks more like the midpoint which would not be accurate. If the intend is using the midpoint to represent the interval width indicate the correct values. If you want to use lower value place them at the beginning of the width, not the middle.

Comment [JK8]: This is not apparent from the chart. See comments above. Table 1 gives a better presentation.

DESCRIPTIVE STATISTICS 6

Figure 2

Scatter Plot Showing the Relationship between the Seating Capacity of and the Number of

People Visiting the Restaurants

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

100

150

200

0 50 100 150 200 250

S e a

ti n

g C

a p

a c it

Number of People Visiting the Restaurants (per day)

The Number of People Visiting the Restaurants and the

Seating Capacity

Comment [JK9]: Good with the creation of the scatter plot.

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.

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.

Comment [JK11]: The reference here is not 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

Number of

people who

visit the

restaurant (per

day)

Average rating

by the

customer (per

day)

Seating

capacity

1 144 170 4 110

2 97 73 2 60

3 130 85 2 72

4 80 75 1 68

5 110 118 4 100

6 124 175 5 130

7 91 182 5 150

8 35 78 3 85

9 128 64 2 60

10 112 94 3 85

11 122 148 4 115

12 61 109 5 128

13 38 79 2 65

DESCRIPTIVE STATISTICS 10

14 138 163 5 125

15 112 175 5 168

16 75 200 5 190

17 128 60 2 50

18 33 81 3 85

19 67 109 4 125

20 75 55 1 60

21 126 112 3 85

22 131 134 5 125

23 67 85 3 72

24 75 108 5 100

25 102 136 5 112

26 82 128 5 150

27 67 54 1 60

28 78 124 4 105

29 92 105 3 85

30 130 138 3 125

31 142 85 2 72

32 90 115 4 125

33 150 197 3 180

34 97 125 5 92

35 123 75 3 60

36 115 152 4 130

37 98 102 5 125

38 76 125 4 155

39 81 138 4 100

40 68 115 2 92

41 108 142 4 112

42 73 95 2 62

43 154 133 5 102

44 116 69 1 55

45 54 85 2 70

46 64 105 5 125

47 148 98 5 102

48 93 146 4 130

49 85 120 5 92

50 107 80 1 72