Statistics Assessment: Analyzing Water Park and Hotel Guest Data

This statistics assessment analyzes data related to water park and hotel guests. The assessment begins with a comparison of visitor demographics, highlighting the water park's suitability for various guest types, based on percentage of visitors. It then delves into statistical concepts, defining and providing examples of population, nominal, and ordinal data. The second part of the assessment focuses on data analysis, including the calculation of mean, median, variance, and standard deviation. An Ogive graph is used to represent cumulative distribution. Quartiles (Q1 and Q3) are calculated, and interpretations are provided. The assessment concludes with calculations of revenue projections based on visitor data and an analysis of visitor spending, with the goal of understanding visitor behavior and financial implications.

Statistics Assessment – Management information
Part 1 A:
Graph for Water Park and Hotel Guests
1a) Explanation:
According to both of the graphs it has been discovered that the water park is suitable because, by
comparing both the % of visitors during its peak season the results shows different percentages
which were higher for the water park then for the hotel guests. According to the data the graph
demonstrates that for Water Park, 25 % of visitors were singles under 25. Whereas 17 % of guests
were singles under 25. Comparing both the results it also shows the following that 12 % of visitors
were singles over 25. In contrast, 9 % of guests were singles over 25 for hotel guests. Furthermore
results show also that for Water Park 6% of visitors were couples under 25 compared to the type of
guests which were couples under 25, only 3% during peak season. Also by looking at the data which
demonstrates that the water park is seen as more suitable and popular for various types of guests.
For example for family groups the water park will be very suitable as 51% of guests during peak
season were family groups at the hotel.

1b)
Population data is one of the ways of collecting statistical data. Population data is known as the
entire set of items or people of interest that you want to target from including its final counts or
measurement. An example of population data according to the graph when collecting data we have
used population data to which include the type of customers and the type of guests and focusing on
the various category of guests. As to find out the overall % of guests during peak season we had to
understand the population.
Nominal data does not have any order on how its data and category is presented such as the way
the variables are presented including gender for example there is no order on how it is presented
male or female they can be on any categories. According to research, nominal data is known as the
lowest form of data since very small can be performed with it e.g. counts and percentages. For
example when relating nominal data on the data we have collected the family category it does not
give data on females and males as it could be any type of families. In addition, similarly for the
categories for singles over and under 25 and couples it does not state whether those singles are
female or male or what percentage of are male or female.
Ordinal data has an order of the way it presents its data categories. It can either start from good to
bad, such as good, average and poor or 1st 2nd 3rd.
Sample data is known as a part interested from the whole population of a group which is known as a
subset.
Part 2A

The distribution of this histogram is positively skewed.
2b:
PART 2
Question 1
Mean – It can be regarded as the average value of a particular set of data. Under this, usually
all the numbers add up and are then divided by the sum of numbers.
Median – It is a measure of central tendency which is regarded as the mid value of the series.
In order to find the median, the numbers of a data set are to be listed in numerical order.
For the given
data set, both the
measures have
been used.
Amount paid
(€)
Number of visitors
(F)
mid-point
(x) Fx fxx
Cummfre
q
Cumm
%
0 0 0 0
35 under 45 102 40 4080
16320
0 102
35.7894
7
45 under 55 74 50 3700
18500
0 176
61.7543
9
55 under 65 58 60 3480
20880
0 234
82.1052
6
65 under 75 46 70 3220
22540
0 280
98.2456
1
75 under 85 5 80 400 32000 285 100
Total 285 14880
81440
0

Mean 52.21053
Variance 131.6048
Standard
deviation 11.47191
Median 45
SIR 10
Q1 37
Q3 57
Max 80
Min 40
Range 40
In the above example, the purpose was to identify how much each visitor pays in
order to visit this park. The value of mean shows that on an average, € 52 has been paid by
every visitor.
0 35 under 45 45 under 55 55 under 65 65 under 75 75 under 85
0
25
50
75
100
Ogive graph
Amount Paid (€)
Cummalative %
In statistics, Ogive is a free hand graph reflecting the curve of a cumulative
distribution function. The plotted points are the upper class limit and the corresponding
cumulative frequencies. The above graph is showing the cumulative distribution at points like
35 under 45, 45 under 55, 55 under 65, 65 under 75 and 75 under 85.
Question 2

Q1 37
Q3 57
Q3 – The third quartile is the upper quartile of the data and it is equal to the 75 th percentile of
the data series. In the above example, the value of Q3 is 57. It denotes that average price paid
by the visitors in 3rd quartile period is €57.
Q1 – The first quartile is the lower quartile of a data series and it is equal to the 25th
percentile. In the given example, the value of the Q1 is 37. It denotes that average price paid
by the visitors in the 1st quartile is €37.
Question 3
Average amount paid by the visitors to the park = €52
Number of expected adult excursions = 6300
The revenue that travel company will take = 52*6300 = 3, 27,600
Question 4
0 35 under 45 45 under 55 55 under 65 65 under 75 75 under 85
0
25
50
75
100
Chart Title
Amount Paid (€)
Cummalative %
From the Ogive graph, it can be stated that 36% of the people paid less than €40.
The calculation can be shown as follows:
Total number of visitors = 285
Number of people who paid less than 40 = 102
Percentage = Number of people paid less than 40 / total number of visitors * 100
= 102 / 285 * 100
= 36%

60 % of the people paid less than 45 and 55 €. Calculation can be shown as follows:
Total number of visitors = 285
60% of total number of visitors = 60% of 285
= 171 people
Therefore, 171 people have paid less than €45 and €55.