Statistics: Measurement and Decision Making

Statistics 1
Measurement and decision making
Name:
College:

Statistics 2
Executive summary
The aim of this business management report is to investigate the relationship between
cow weight and the milk fat content for a sample data from (.........) farm. The data will be
analyzed using several descriptive and inferential statistics methods in order any emerging trends
or consistent characteristics which can then be used to forecast ways of reducing the fat content
to within acceptable limits. This is necessary if the farms products are to remain competitive and
hence profitable considering the current market dynamics. Statistical analysis will help us to
draw meaningful conclusions and to put forward useful recommendations which can help the
farm meet set objectives. Several data analysis techniques were used to analyze the provided
dataset in order to give it some practical interpretation and meaning. The mean and median were
the two main measures of central tendency applied to indicate the centre of the data distribution.
For the measures of variability, the standard deviation and the range of the values were used for
variation analysis. A higher variability is interpreted to mean that the values of the data set are
very different and that it there is higher probability of encountering extreme values. A lower
variability on the other hand is indicative of a low spread and the values will be more almost
similar. Simple linear regression model was used to fit the data set because it is easy to
understand and also intuitive in nature. Linear regression was used to investigate the connection
that exists between cow weight and the weekly average fat content in the milk. Despite that
simple linear regression does not fit the data always, it clearly shows the connection between any
two variables. For the analysis of the discrete data variable, Poisson distribution was used.
Poisson distribution is a powerful analysis tool that can provide business solutions to improve
efficiency. For instance, it can be used to determine whether it is profitable to keep a business
open throughout the day. Several methods of inferential statistics were used to analyze the data
to enable us to arrive at meaningful conclusions regarding the populations the sample was
obtained from. These include the t-distribution, confidence intervals and the regression analysis
mentioned above.

Statistics 3
Table of Contents
Executive summary.........................................................................................................................2
Introduction......................................................................................................................................4
1 Descriptive statistics.....................................................................................................................4
1.1 Measures of central tendency.................................................................................................4
2 Inferential statistics.......................................................................................................................5
2.1 Measures of variation.............................................................................................................5
3 Probability distributions................................................................................................................8
3.1 Discrete probability distributions...........................................................................................8
3.2 Continuous probability distributions......................................................................................9
3.3 Skewness..............................................................................................................................11
3.4 Kurtosis................................................................................................................................12
4 Linear regression analysis...........................................................................................................13
Conclusion.....................................................................................................................................15
References......................................................................................................................................16

Statistics 4
Introduction
Many physical and practical phenomena we encounter in our everyday lives can be
analyzed using the various methods of statistical analysis available to extract from them
meaningful information which can then be used to improve their performance. This certainly true
for many businesses and business ventures whose main objective is to reap maximum benefits
from their firms while at the same time keeping their operations in accordance with set laws and
obligations.
1 Descriptive statistics
The analysis of data in such a way that meaningful patterns emerge from the data
summary is called descriptive statistics. Descriptive statistics present a quantitative measure of
the features or a particular data. In descriptive statistics, a data sample is summarized instead of
using the sample data to present the characteristics of the population represented by the sample.
However, descriptive statistics does not give us power to draw useful conclusions concerning
hypothesis tests (Gelman & Nolan, 2017).
Descriptive statistics measures include: central tendency measures and dispersion measures.
1.1 Measures of central tendency
Central tendency is a division of descriptive statistics. It summarizes a collection of data
values via a single data item that shows the midpoint of the distribution of the data set. Central
tendency measures include the mean, mode and the median. Despite the fact that central
tendency does not give any information concerning the independent data values, it provides a
complete summary of the entire set of values.
i) Mean
Also referred to as the average, the mean is a widely used measure of central tendency.
Its nature allows it to be applied on both continuous and discrete data values. The mean of a
dataset is the value that results in the smallest magnitude of deviation (error) from all the other
data values in the set. The mean can be defined for a data sample and also for a population.
However, they are both calculated using the same formula:
Mean = ∑ x
n
Where x is the total sum of the items in the data set and n represents the total count of the data
items.
From our data, the mean cow weight is obtained as follows:
Mean cow weight (kg) = ∑ of all cow weights
total number of cows = 21534.71
50 = 430.69 kg
Therefore the mean cow weight is 430.69 kg
ii) The median