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Descriptive Statistics – categorical variables: Region

Descriptive Statistics – categorical variables: Region

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Produce one cross tabulation (what is cross tabulation) in order to investigate any possible association between two appropriate categorical variables.

Comment on the results and make relevant recommendation to Hotel’s management

According to the data which given on the pages ??, which data was provided by 104 hotels. After collected the 104 surveys from the hotels, found two outline data on -1 data on distance from the nearest from the rail link and -1 data on the service years of the hotel managers. So, we decided ignore these two surveys data. However, the total of the surveys from the hotels are 102 only.

 

Region
Mean1.892156863
Standard Error0.081133092
Median2
Mode1
Standard Deviation0.819404067
Sample Variance0.671423025
Kurtosis-1.482360029
Skewness0.203161078
Range2
Minimum1
Maximum3
Sum193
Count102
CountryNo. of Hotel
1- Finland40
2 – Sweden33
3 – Norway29
 Total102

The total of the hotel is 102, 40 of the hotels are located in Finland, it is 39% of the total.

The second one 33 hotels are located in Sweden, 32 % of the total. Norway is 29% of the total, only 29 hotels in there.

Descriptive Statistics – categorical variables: Size of the Hotel

Size of Hotel
Mean1.81372549
Standard Error0.080921686
Median2
Mode1
Standard Deviation0.817268963
Sample Variance0.667928558
Kurtosis-1.413014183
Skewness0.358131814
Range2
Minimum1
Maximum3
Sum185
Count102
No. of roomsNo. of Hotel
1 = < 5045
2 = 50-10031
3 = >10026
 Total102

This figure shows that 45 Hotels of the total 102 is less that 50 rooms, 44% of the total.

Only 26% of the Hotels are operating more than 100 rooms.

Descriptive Statistics – categorical variables: Gender of the manager

Gender of the manager
Mean1.411764706
Standard Error0.04897105
Median1
Mode1
Standard Deviation0.494583357
Sample Variance0.244612697
Kurtosis-1.905300144
Skewness0.363942696
Range1
Minimum1
Maximum2
Sum144
Count102
Gender of managerNo. of person
1-  Male60
2- Female42
Total102

In 102 hotel managers, 60 managers are male to take 59% of the total. The rest of 41% managers are female.

Descriptive Statistics – Categorical variables: Years of service

Years of service
Mean1.519607843
Standard Error0.061890228
Median1
Mode1
Standard Deviation0.625060665
Sample Variance0.390700835
Kurtosis-0.353077889
Skewness0.793077803
Range2
Minimum1
Maximum3
Sum155
Count102
Service yearsNo. of manager
1 = 0-3 years56
2 = 4-7 years39
3 = > 7 years7
Total 102

The survey of the service year is 55% of the managers are working in the hotel between 0-3 years. Less than 7% of the managers are working over 7 years.

Descriptive Statistics – numerical variables: Distance

Firstly, the categorical variables which are: Distance, Advertising, Employees, Type A and B.

 

Distance (miles)
Mean2.431372549
Standard Error0.091962262
Median2.5
Mode1.5
Standard Deviation0.92877332
Sample Variance0.86261988
Kurtosis-1.097970621
Skewness0.062529806
Range3.5
Minimum0.5
Maximum4
Sum248
Count102
Distance (miles)frequency
0.5-11
1-1.515
1.5-216
2-2.518
2.5-315
3-3.517
3.5-420
Grand Total102

According to the Distance (in miles) chart, the nearest distance between hotel and rail link is 0.5 miles, the longest distance is 4 miles, the mode is 1.5 miles.

The mean is 2.43 and the median is 2.5, figures are closed together.

Descriptive Statistics – numerical variables: Advertising

Advertising (£)
Mean1223.04902
Standard Error28.70686225
Median1198.5
Mode1460
Standard Deviation289.9250971
Sample Variance84056.56193
Kurtosis-1.113213947
Skewness0.020149338
Range1147
Minimum651
Maximum1798
Sum124751
Count102
Advertisingfrequency
600-6991
700-7992
800-89920
900-9993
1000-109911
1100-119914
1200-12997
1300-139910
1400-149915
1500-159911
1600-16992
1700-18006
Grand Total102

The Advertising (£) table showing that the mode of the hotel where spend on advertising average per month is £1460.00. The maximum spends on advertising(£1798.00) are almost 2.5 times of the minimum spending (£651.00).

 

Descriptive Statistics – numerical variables: Employees

Employees
Mean19.26470588
Standard Error0.610356244
Median18
Mode15
Standard Deviation6.164295902
Sample Variance37.99854397
Kurtosis-0.707479275
Skewness0.654287392
Range24
Minimum10
Maximum34
Sum1965
Count102
Employeesfrequency
10-1211
13-1526
16-1819
19-2117
22-245
25-276
28-3014
31-333
34-361
Grand Total102

The maximum of employees who works in hotel is 34, the minimum of the manpower of the hotel is 10 only. It is different in 3.5 times between in maximum and minimum.

The median is 18 employees and the mode is 15 employees, these two figures are closed.

Descriptive Statistics – numerical variables: Accommodation A

Accommodation type A
Mean398020.5882
Standard Error8876.553606
Median387000
Mode414000
Standard Deviation89648.79698
Sample Variance8036906800
Kurtosis-0.77256128
Skewness0.260649865
Range390000
Minimum253000
Maximum643000
Sum40598100
Count102
Income of Type Afrequency
250000-29999920
300000-34999912
350000-39999921
400000-44999918
450000-49999915
500000-54999911
550000-5999994
600000-6500001
Grand Total102

Descriptive Statistics – numerical variables: Accommodation B

Accommodation type B
Mean212133.3333
Standard Error729.3568615
Median211750
Mode208500
Standard Deviation7366.143225
Sample Variance54260066.01
Kurtosis-0.687049798
Skewness0.262688332
Range31200
Minimum198300
Maximum229500
Sum21637600
Count102
Income of Type Bfrequency
195000-1999993
200000-20499915
205000-20999925
210000-21499924
215000-21999917
220000-22499914
225000-2300004
Grand Total102

This table shows the 104 hotels they got the similar on the average monthly income from the accommodation A and B.

Investigate of relationship between Region and Size of Hotel

We are choosing region of the hotel located and the size of the hotel to investigate ant possible association from the categorical variables.

Our hypothesis is set as below:

: No relationship between the room size and the hotel located in country.

: There is a relationship between the room size and the hotel located in country.

According to the data are given from Region and Size of the hotel, we are organizing as the below table:

Size of the Hotel
smallmediumlarge
<5050-100>100region
1-FINLAND1320740
2-SWEDEN187833
3-NORWAY1441129
Total453126102

So, base the on above table, we change to the observe value as below table:

Observe valueSMLTTL
1-FINLAND1320740
2-SWEDEN187833
3-NORWAY1441129
 Total453126102

Then, we start to calculate the expected value, for example,

Expected valueSMLTTL
1-FINLAND=40/102*45=40/102*31=40/102*2640
2-SWEDEN=33/102*45=33/102*31=33/102*2633
3-NORWAY=29/102*45=29/102*31=29/102*2629
 Total453126102

After that, we got the figure as below table

Expected valueSMLTTL
1-FINLAND17.6470588212.1568627510.1960784340
2-SWEDEN14.5588235310.029411768.41176470633
3-NORWAY12.794117658.813725497.39215686329
 Total453126102

The Chi-square test statistics:

(
1317.64705882-4.64705882421.595155711.22372549
2012.156862757.84313725561.5148025.060088552
710.19607843-3.19607843110.214917341.001847662
1814.558823533.44117647111.84169550.813368984
710.02941176-3.0294117659.177335640.915042263
88.411764706-0.4117647060.1695501730.020156314
1412.794117651.2058823531.4541522490.113657877
48.81372549-4.8137254923.171953092.62907588
117.3921568633.60784313713.01653211.760857128
Total 10213.53782015

Due to the degree of freedom is = (m-1) (n-1) = (3-1) (3-1) = 4, so that, the critical value of 5% on 4 degree of freedom is 9.488.

Since 13.53782015 is greater than 9.488, we reject .

We conclude that there is a relationship between the room size and the hotel located in country.

Relationship between the total average monthly incomes and distance of the hotel from the nearest rail link

Total we have 102 surveys of hotel,  After group the data of total average income and distance of the hotel from the nearest rail link, the figure shown as below table:

xyxyx2y2
Distance Type A Type B Total income of A + BColumn3Column1Column2
11.547300021300068600010290002.254.70596E+11
22.7526300019830046130012685757.56252.12798E+11
3142300021200063500063500014.03225E+11
42.626340019900046240012022406.762.13814E+11
52.434200021050055250013260005.763.05256E+11
62.0536350020650057000011685004.20253.249E+11
70.55180002076007256003628000.255.26495E+11
8148930021950070880070880015.02397E+11
93.45281000204000485000167325011.90252.35225E+11
101.24910002285007195008634001.445.1768E+11
913.7309600208100517700191549013.692.68013E+11
921.549600021850071450010717502.255.1051E+11
933329000206000535000160500092.86225E+11
942.536600020850057450014362506.253.3005E+11
953.5286100201700487800170730012.252.37949E+11
962.2528690020250048940011011505.06252.39512E+11
971.254730002084006814008517501.56254.64306E+11
981.553700021750075450011317502.255.6927E+11
992440000218700658700131740044.33886E+11
1002414000217000631000126200043.98161E+11
1012.626340019900046240012022406.762.13814E+11
1023446000212400658400197520094.33491E+11
Sum24862235700144416375690.1053.89007E+13

n = 102                        Σx = 248          Σy = 62235700            Σxy = 144416375

= 690.105                         = 3.89E+13

r =                                  = -703983350

= 8886.71

= 9.46E+13

= 916834454

r = -0.76784129

So that, base on the general interpretation of Correlation coefficient, we got the figure is

-0.76784129, that means that there is no relationship between the total average monthly incomes and the distance of the hotel from the nearest rail link.

Descriptive Statistics – categorical variables: Region

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Last Updated on February 14, 2019

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