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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 Mean 1.892156863 Standard Error 0.081133092 Median 2 Mode 1 Standard Deviation 0.819404067 Sample Variance 0.671423025 Kurtosis -1.482360029 Skewness 0.203161078 Range 2 Minimum 1 Maximum 3 Sum 193 Count 102
 Country No. of Hotel 1- Finland 40 2 – Sweden 33 3 – Norway 29 Total 102

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 Mean 1.81372549 Standard Error 0.080921686 Median 2 Mode 1 Standard Deviation 0.817268963 Sample Variance 0.667928558 Kurtosis -1.413014183 Skewness 0.358131814 Range 2 Minimum 1 Maximum 3 Sum 185 Count 102
 No. of rooms No. of Hotel 1 = < 50 45 2 = 50-100 31 3 = >100 26 Total 102

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 Mean 1.411764706 Standard Error 0.04897105 Median 1 Mode 1 Standard Deviation 0.494583357 Sample Variance 0.244612697 Kurtosis -1.905300144 Skewness 0.363942696 Range 1 Minimum 1 Maximum 2 Sum 144 Count 102
 Gender of manager No. of person 1-  Male 60 2- Female 42 Total 102

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 Mean 1.519607843 Standard Error 0.061890228 Median 1 Mode 1 Standard Deviation 0.625060665 Sample Variance 0.390700835 Kurtosis -0.353077889 Skewness 0.793077803 Range 2 Minimum 1 Maximum 3 Sum 155 Count 102
 Service years No. of manager 1 = 0-3 years 56 2 = 4-7 years 39 3 = > 7 years 7 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) Mean 2.431372549 Standard Error 0.091962262 Median 2.5 Mode 1.5 Standard Deviation 0.92877332 Sample Variance 0.86261988 Kurtosis -1.097970621 Skewness 0.062529806 Range 3.5 Minimum 0.5 Maximum 4 Sum 248 Count 102
 Distance (miles) frequency 0.5-1 1 1-1.5 15 1.5-2 16 2-2.5 18 2.5-3 15 3-3.5 17 3.5-4 20 Grand Total 102

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 (£) Mean 1223.04902 Standard Error 28.70686225 Median 1198.5 Mode 1460 Standard Deviation 289.9250971 Sample Variance 84056.56193 Kurtosis -1.113213947 Skewness 0.020149338 Range 1147 Minimum 651 Maximum 1798 Sum 124751 Count 102
 Advertising frequency 600-699 1 700-799 2 800-899 20 900-999 3 1000-1099 11 1100-1199 14 1200-1299 7 1300-1399 10 1400-1499 15 1500-1599 11 1600-1699 2 1700-1800 6 Grand Total 102

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 Mean 19.26470588 Standard Error 0.610356244 Median 18 Mode 15 Standard Deviation 6.164295902 Sample Variance 37.99854397 Kurtosis -0.707479275 Skewness 0.654287392 Range 24 Minimum 10 Maximum 34 Sum 1965 Count 102
 Employees frequency 10-12 11 13-15 26 16-18 19 19-21 17 22-24 5 25-27 6 28-30 14 31-33 3 34-36 1 Grand Total 102

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 Mean 398020.5882 Standard Error 8876.553606 Median 387000 Mode 414000 Standard Deviation 89648.79698 Sample Variance 8036906800 Kurtosis -0.77256128 Skewness 0.260649865 Range 390000 Minimum 253000 Maximum 643000 Sum 40598100 Count 102
 Income of Type A frequency 250000-299999 20 300000-349999 12 350000-399999 21 400000-449999 18 450000-499999 15 500000-549999 11 550000-599999 4 600000-650000 1 Grand Total 102

Descriptive Statistics – numerical variables: Accommodation B

 Accommodation type B Mean 212133.3333 Standard Error 729.3568615 Median 211750 Mode 208500 Standard Deviation 7366.143225 Sample Variance 54260066.01 Kurtosis -0.687049798 Skewness 0.262688332 Range 31200 Minimum 198300 Maximum 229500 Sum 21637600 Count 102
 Income of Type B frequency 195000-199999 3 200000-204999 15 205000-209999 25 210000-214999 24 215000-219999 17 220000-224999 14 225000-230000 4 Grand Total 102

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 small medium large <50 50-100 >100 region 1-FINLAND 13 20 7 40 2-SWEDEN 18 7 8 33 3-NORWAY 14 4 11 29 Total 45 31 26 102

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

 Observe value S M L TTL 1-FINLAND 13 20 7 40 2-SWEDEN 18 7 8 33 3-NORWAY 14 4 11 29 Total 45 31 26 102

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

 Expected value S M L TTL 1-FINLAND =40/102*45 =40/102*31 =40/102*26 40 2-SWEDEN =33/102*45 =33/102*31 =33/102*26 33 3-NORWAY =29/102*45 =29/102*31 =29/102*26 29 Total 45 31 26 102

After that, we got the figure as below table

 Expected value S M L TTL 1-FINLAND 17.64705882 12.15686275 10.19607843 40 2-SWEDEN 14.55882353 10.02941176 8.411764706 33 3-NORWAY 12.79411765 8.81372549 7.392156863 29 Total 45 31 26 102

The Chi-square test statistics:

 ( 13 17.64705882 -4.647058824 21.59515571 1.22372549 20 12.15686275 7.843137255 61.514802 5.060088552 7 10.19607843 -3.196078431 10.21491734 1.001847662 18 14.55882353 3.441176471 11.8416955 0.813368984 7 10.02941176 -3.029411765 9.17733564 0.915042263 8 8.411764706 -0.411764706 0.169550173 0.020156314 14 12.79411765 1.205882353 1.454152249 0.113657877 4 8.81372549 -4.81372549 23.17195309 2.62907588 11 7.392156863 3.607843137 13.0165321 1.760857128 Total 102 13.53782015

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:

 x y xy x2 y2 Distance Type A Type B Total income of A + B Column3 Column1 Column2 1 1.5 473000 213000 686000 1029000 2.25 4.70596E+11 2 2.75 263000 198300 461300 1268575 7.5625 2.12798E+11 3 1 423000 212000 635000 635000 1 4.03225E+11 4 2.6 263400 199000 462400 1202240 6.76 2.13814E+11 5 2.4 342000 210500 552500 1326000 5.76 3.05256E+11 6 2.05 363500 206500 570000 1168500 4.2025 3.249E+11 7 0.5 518000 207600 725600 362800 0.25 5.26495E+11 8 1 489300 219500 708800 708800 1 5.02397E+11 9 3.45 281000 204000 485000 1673250 11.9025 2.35225E+11 10 1.2 491000 228500 719500 863400 1.44 5.1768E+11 91 3.7 309600 208100 517700 1915490 13.69 2.68013E+11 92 1.5 496000 218500 714500 1071750 2.25 5.1051E+11 93 3 329000 206000 535000 1605000 9 2.86225E+11 94 2.5 366000 208500 574500 1436250 6.25 3.3005E+11 95 3.5 286100 201700 487800 1707300 12.25 2.37949E+11 96 2.25 286900 202500 489400 1101150 5.0625 2.39512E+11 97 1.25 473000 208400 681400 851750 1.5625 4.64306E+11 98 1.5 537000 217500 754500 1131750 2.25 5.6927E+11 99 2 440000 218700 658700 1317400 4 4.33886E+11 100 2 414000 217000 631000 1262000 4 3.98161E+11 101 2.6 263400 199000 462400 1202240 6.76 2.13814E+11 102 3 446000 212400 658400 1975200 9 4.33491E+11 Sum 248 62235700 144416375 690.105 3.89007E+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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