Data Analysis and Statistics

DATA ANALYSIS
STATISTICS
STUDENT ID:
[Pick the date]

Introduction
The objective of the given report is to provide the result of data analysis with regards to data
pertaining to coffee shop based on the application of appropriate statistical techniques. The given
report also provides some theoretical background with regards to normal distribution and also an
inferential statistical technique which is confidence interval. The data in the context of coffee
shop relates to food preparation time and the customer behavior. The former provides
information about the staff and their efficiency in terms of time required to prepare various items
on the menu. The latter provides information pertaining to behavior of customer in terms of
purchasing decision and time spent in the coffee shop. A continuous random variable has been
selected from the food preparation time which relates to the latte preparation time. Further, a
discrete variable has been selected from customer behavior which relates to the sugar sachet
purchased by the consumers per order. The confidence interval for the mean of both selected
variables has been estimated as part of the report which may be useful for the management in
taking suitable decisions to enhance efficiency and profitability of the coffee shop.
Analysis
a) (i) For facilitating analysis of various populations, suitable samples are drawn and requisite
inferential statistical techniques are applied based on the underlying probability distribution
associated with the sample. One of the most common sampling distributions is normal
distribution. This may be defined as a continuous probability distribution which is symmetric
about the mean and tends to represent itself in a form of a bell curve. This implies that as one
moves away from the mean, the probability of finding a particular value decreases (Flick,
2015). This is evident from the following graphical illustration.

(ii) It is quite common to use normal distribution for expressing sampling distributions. One of
the key reasons is the ease to use of this distribution for further analysis since only mean and
standard deviation are required to express the same. Based on these two parameters, it is possible
to express the probability associated with a given value and thereby determine the likelihood of
the same (Hillier, 2016). Additionally, a host of variables tend to mirror normal distribution in
actuality owing to which it makes sense to use normal distribution for analyzing the sample as
well. Further, normal distribution can also be approximated to discrete probability distributions
such as binomial and poisson which further enhances the utility of this probability distribution
(Medhi, 2016). It is imperative to note that skew for normal distribution is zero as also apparent
from the above illustration since the graphical representation is symmetrical about the mean.
Further, a kurtosis value of 3 is observed for normal distribution which highlights the appropriate
height and thickness of the peak (Taylor and Cihon, 2017).
(iii) The basis for inferential statistics lies in the fact that the sample population tends to
considered as a faithful representation of the overall population and thereby by deploying
techniques such as confidence interval, hypothesis testing, it is possible to derive meaningful
conclusions about the population characteristics with a reasonable accuracy (Hair et. al., 2015).
This is highly useful for analysis since the researcher instead of measuring a given characteristic
for the whole population can do so reasonably with the use of a representative sample. This leads
to saving in both costs and time on the part of the researcher. However, lack of a representative
sample could lead to wrong conclusions being drawn from the inferential statistics analysis
(Lind, Marchal, and Wathen, 2015).