Problem Solving

Use the hotel prices data set (attached) and answer the following questions:What was the average price of a room at two-star, three-star and four-star hotels around the world during the first half of 2013. The dataset contains prices in English pounds. Complete the following for the two-star, three-star and four-star hotels.
The Average price of rooms for each hotel rank is represented on Table 1below;
Table1 below indicates that the average price for a Two-star Hotel is ₤65, for the Three Star is ₤89, and for the Four-Star hotels is ₤127.
Table1: Average Hotel Price
Two Star Three Star Four Star
65 89 127
Therefore, the results of the analysis indicate that most of Two-star Hotels are cheaper, while Most of the Three-star hotels are affordable. However, the results of the data imply that Four-Star Hotels around the world are expensive.
a. Compute the mean, median, first quartile and third quartile.
The analysis found that the Mean price for all the hotels is ₤94, Median is ₤85, 1st Quartile is ₤70, while the 3rd quartile is ₤115.
Table2: Central Tendency
Statistics Values
Mean 94
Median 85
1st Quartile 70
3rd Quartile 115
Therefore, there is a 75% probability of getting a hotel with prices between ₤70 and ₤115.
b. Compute the range, interquartile range, variance, standard deviation and coefficient of variation. 
Table3: Central Tendency
Statistics
Mean 94.2
Standard Deviation 39.8
Variance 1587.8
Range 184.0
1st Quartile 69.5
3rd Quartile 115
Interquartile Range 45.5
Coefficient of Variation 0.

42
c. Interpret the measures of central tendency and variation within the context of this problem.
Computations from the analysis Table 3 above, Central Tendency indicate that the mean for hotels around the world is ₤94. Although all the hotel samples have average price is (<94), they have a relatively higher sample standard deviation (SD = 39.8). This means there is a wider range of hotel pricing among the three hotel categories, which included Two, Three, and Four Star Hotels. Similarly, we may claim that Four Star Hotel charges are high which creates a high sample variation (Variance=1587.8).
Various explanations can be provided. For instance, four-star hotel bills are high because of the room’s luxuriousness, which comes with lavish amenities, spacious with better foods and refreshments. The range between hotel prices is ₤46 (Interquartile Range=45.5) with a75% chance of getting a hotel with the prices of between ₤69 and ₤115. Also, coefficient variation is 0.42, implying that the level of dispersion around the average price is high.
d. Construct a boxplot. Are the data skewed? If so, how? 

Figure1: Boxplot for Hotel Prices
Figure1 above show a Boxplot for the samples Hotel prices. Based on the plot, the hotel prices data are skewed to the right. Which suggests that the median is slightly lower than the mean. The results are consistent with the central tendency measure which also found the median to be lower than the mean (Median= 85 and Mean=94).
e. Based on the results of (a) through (c), what conclusions can you reach concerning these variables? In summary, the results for the variable above indicate that there is a significant variation between hotel prices. With a Four-star hotel charging high prices than the rest. The lowest price for the sampled hotel is ₤63. While the highest is ₤115. The distribution of data in the variables also suggests that the data is skewed to the right.
For questions (a) and (b), students are required to do calculations in Excel.For questions (d), students are to use the boxplot maker for this assignment.These graphs are to be copied/pasted in a Word document. Students are required to write at least a 3 sentence explanation each for parts (c) to (e)
City Two-Star Three-Star Four-Star
Amsterdam 74 88 116
Bangkok 23 35 72
Barcelona 65 90 106
Beijing 35 50 79
Berlin 63 58 76
Boston 102 132 179
Brussels 66 85 98
Cancun 42 85 205
Chicago 66 115 142
Dubai 84 67 111
Dublin 48 66 87
Edinburgh 72 82 104
Frankfurt 70 82 107
Hong Kong 42 87 131
Istanbul 47 77 91
Las Vegas 41 47 85
Lisbon 36 56 74
London 74 90 135
Los Angeles 80 118 200
Madrid 47 66 79
Miami 84 124 202
Montreal 76 113 148
Mumbai 41 72 90
Munich 79 97 115
New York 116 161 206
Nice 69 87 133
Orlando 45 78 120
Paris 76 104 150
Rome 75 82 108
San Francisco 92 137 176
Seattle 95 120 166
Shanghai 22 49 79
Singapore 58 104 150
Tokyo 50 82 150
Toronto 72 92 149
Vancouver 74 105 146
Venice 87 99 131
Washington 85 128 158
Appendixes:
Double click on the Icon below to open the Excel file with calculations