Applied Quantitative Methods: Mean, Median, Mode, Standard Deviation, Inter-quartile Range

Applied Quantitative Methods

Table of Contents
INTRODUCTION...........................................................................................................................3
Question 1........................................................................................................................................3
c. On the basis of the raw data calculation of the mean, median and the mode..........................5
Question 2........................................................................................................................................9
a. Stating the difference between the sample and the population................................................9
b. Calculation of the standard deviation of an annual sales ......................................................10
c. Computing inter-quartile range relating to the annual advertising expenses ........................11
d. Computing coefficient of the correlation ..............................................................................12
Question 3......................................................................................................................................13
a. Explaining a selection of the dependent and an independent variable among the dataset of
annual sales and annual advertising expenses ..........................................................................13
b. Computing regression equation and interpreting the results .................................................14
c. Presenting an evaluation of coefficient determination and interpreting the finding
accordingly in order to analyse the dataset regarding the annual sales and the promotional
expenses.....................................................................................................................................16
Question 4......................................................................................................................................16
a. Calculating the probability ....................................................................................................17
b. ................................................................................................................................................17
c..................................................................................................................................................17
d. Explaining the relationship between recruitment and training .............................................18
Question 5......................................................................................................................................18
a..................................................................................................................................................18
b. ................................................................................................................................................19
CONCLUSION..............................................................................................................................19
REFERENCES................................................................................................................................1

INTRODUCTION
Quantitative methods details the different statistical and mathematical tools that are used
to analyse the numerical information that has been collected and then a synopsis is presented.
The statistical tools help in analysing the data that has been collected and then the results hence
drawn are interpreted accordingly (Liu and et.al., 2018). In the current report, the numerical data
has been assessed using different statistical concepts. Initially, the concept of frequency
distribution has been used and a histogram will be presented for the data related to the
restaurants. Then, the report will involve calculation of standard deviation and the correlation
coefficient will be calculated based on the data presented. The report will also present a
regression analysis and the coefficient of determination will be calculated for the advertising
expenditure that company incurred and the sales concurrent. In the next section, the report will
calculate probability of the cricket team by analysing the training and the associated recruitment.
Finally, the report will identify whether r z test can be applied on a non-normal distribution and
the situation of hedge fund manager will be analysed.
Question 1
Frequency distribution- It is the table that depicts a frequency of the several outcomes in
the sample. Each and every entry in a table reflects a frequency or the count of an occurrences of
the values in the particular or the specific group. The table below summarizes distribution of the
values within the sample. In the statistics, the table of the frequency distribution tells about the
number of an occurrences by way of organizing the raw data in an appropriate manner.
Count of City restaurant
City restaurant
Freq
uenc
y
25-34 8
35-44 12
45-54 13
55-64 9
65-74 3
75-84 2

85-94 3
Grand Total 50
Count of Suburban
restaurant
Suburban restaurant
Freq
uenc
y
27-36 10
37-46 21
47-56 13
57-66 2
67-76 2
77-86 1
87-96 1
Grand Total 50
Interpretation- The table presented above shows the frequency distribution of both types
of the restaurant that is City and the Suburban restaurant. As per the 50-sample taken of the city
restaurant the highest frequency resulted as 13 that lies between the class interval of 45-54 and
the lowest frequency as 2 that is the range of 75-84. Similarly, by reviewing the frequency
distribution of Suburban restaurant the highest and the lowest value of frequency resulted as 21
and 1 that lies in a range of 37-46 & 87-96.
Cumulative and relative frequency
Suburban
restaurant Total
Cumulative
frequency
Relative
frequency Mid-point
27-36 10 10 0.2 45
37-46 21 31 0.42 60
47-56 13 44 0.26 75
57-66 2 46 0.04 90
67-76 2 48 0.04 105
77-86 1 49 0.02 120

87-96 1 50 0.02 135
Grand
Total 50 100 1
City
restaurant Total
Cumulative
frequency Relative frequency
25-34 8 8 0.16 42
35-44 12 20 0.24 57
45-54 13 33 0.26 72
55-64 9 42 0.18 87
65-74 3 45 0.06 102
75-84 2 47 0.04 117
85-94 3 50 0.06 132
Grand
Total 50 100 1
c. On the basis of the raw data calculation of the mean, median and the mode
Mean- It refers to the mathematical average of the set of a two and more of the numbers.
The mean for given dataset could be computed in various ways with an inclusion of an arithmetic

mean that uses sum of a number in a particular series (George and Mallery, 2016). It is counted
as an indicator which could be used by the firm for the purpose of analysing its performance.
Median- It refers to the middle number or value that is sorted in an ascending form, list of
the numbers could be more descriptive of a specific data than an average. It is used as the
opposed to the value of mean within which the outliers are seen in a sequence that may skew
average values.
Mode- It means the number which appears several numbers of time in the dataset. A
number might be having one modal value and more than one modal value.
S.no City restaurant
1 25
2 51
3 51
4 63
5 45
6 44
7 45
8 49
9 79
10 55
11 28
12 61
13 66
14 27
15 42
16 46
17 55
18 27
19 32
20 40
21 51