Descriptive Statistics Assignment - Statistical Analysis Report

This assignment delves into descriptive statistics, covering various aspects such as levels of measurement (nominal, ratio), and analysis of data using measures like mean, median, standard deviation, and range. The assignment analyzes a dataset on accidents, comparing male and female accident rates, and also investigates salary data. It includes tables summarizing descriptive statistics and interpretations of the results, including the identification of skewness in a histogram. The solution addresses multiple questions, providing detailed explanations of statistical concepts and their application to real-world scenarios. The analysis includes the identification of the level of measurement for different variables, calculation and interpretation of various statistical measures, and visualization of the data using a histogram with a normal curve. The assignment also explores the concept of standard deviation and its interpretation in relation to the spread of data around the mean. The document demonstrates a comprehensive understanding of descriptive statistics and its application in data analysis.

Running head: DESCRIPTIVE STATISTICS
Descriptive Statistics
Name of the Student
Name of the University
Course ID

1DESCRIPTIVE STATISTICS
Table of Contents
Assignment 2: Descriptive Statistics...............................................................................................2
Part 1............................................................................................................................................2
Part 2............................................................................................................................................3
Answer to question 1...............................................................................................................3
Answer to question 2...............................................................................................................4
Answer to question 3...............................................................................................................4
Answer to question 4...............................................................................................................5
Reference.........................................................................................................................................6

2DESCRIPTIVE STATISTICS
Assignment 2: Descriptive Statistics
Part 1
There are four standard level of measurement or scale of measurement which are nominal
level, ordinal level, interval level and ratio level.
The level off measurement for “Gender”, “Age” and “Accident” are nominal level, ratio
level and ratio level respectively.
The below table describes the variable accident for the categorical variable gender. Here,
mean, median, standard deviation, range and sum of accidents are recorded for male and female.
The sample size for the male and female is 250. There are no missing values hence the
population is 500. The mean and median value of accidents for male is 1.98 and 2 respectively.
The range and number of accidents for male is 7 and 1.608 respectively. The mean and median
of accidents for the female is 1.47 and 1 respectively. The range and number of accidents for
female is 6 and 1.412 respectively (Chatfield, 2018). The mean value for male and female is 1.98
and 1.47 which indicates that on an average male faces more accidents than female.
Table 1: Descriptive statistics for the accidents across gender.
Case Processing Summary
Sex of insured Cases
Valid Missing Total
N Percent N Percent N Percent
Number of accidents past
5 years
Male 250 100.0% 0 0.0% 250 100.0%
Female 250 100.0% 0 0.0% 250 100.0%
Descriptives
Sex of insured Statistic Std. Error

3DESCRIPTIVE STATISTICS
Number of accidents past 5
years
Male
Mean 1.98 .102
95% Confidence Interval for
Mean
Lower Bound 1.78
Upper Bound 2.18
5% Trimmed Mean 1.87
Median 2.00
Variance 2.586
Std. Deviation 1.608
Minimum 0
Maximum 7
Range 7
Interquartile Range 2
Skewness .805 .154
Kurtosis .176 .307
Female
Mean 1.47 .089
95% Confidence Interval for
Mean
Lower Bound 1.29
Upper Bound 1.64
5% Trimmed Mean 1.36
Median 1.00
Variance 1.993
Std. Deviation 1.412
Minimum 0
Maximum 6
Range 6
Interquartile Range 2
Skewness .933 .154
Kurtosis .324 .307
Part 2
Answer to question 1
The level of measurement for the salary is ratio level. The level of measurement for the
individual is nominal level.

4DESCRIPTIVE STATISTICS
Answer to question 2
The table 2 contains the mean, median, mode, standard deviation, minimum and
maximum value of the salary of individual.
The mean value of the salary is 34183.7 unit. The median of the salary is 32648.5 unit.
There are more than one mode of the salary and the minimum of the mode is 25153 unit. The
standard deviation is 6294.14 unit (Pyrczak, 2016). The minimum value of the salary is 25153
unit and the maximum value of the salary is 50389.
Table 2: Descriptive statistics for the salary of individuals
Statistics
Salary of an Individual
N Valid 50
Missing 0
Mean 34183.7000
Median 32648.5000
Mode 25153.00a
Std. Deviation 6294.14348
Minimum 25153.00
Maximum 50389.00
a. Multiple modes exist. The smallest value is shown
Answer to question 3
The standard deviation of a variable presents the average distance of the values of
variable from the mean of variable. A higher standard deviation presents that the data is more
spread the mean value and the low standard deviation presents that the data is closer to the mean
value (Holcomb, 2016).

5DESCRIPTIVE STATISTICS
The standard deviation of the salary of individual is 6294.14 unit. This indicates that the
average distance from the mean value of the salary. In other words, the salary of any individual
is on an average 6294.14 units away from the mean salary 34183.7 unit.
Answer to question 4
The histogram with the normal curve is prepared for the distribution of the salary. The
figure 1 presents the histogram. First of all, the histogram is not symmetric, it has a right tail.
This implies the distribution is right skewed. Now, the histogram of the distribution exceeds the
normal curve in the left side. This indicates the lower value of the median than the mean which is
supported by the computed descriptive statistics (Silverman, 2018). In a skewed distribution,
mean and median both can be used as an identical center point depending on the nature of the
skeweness.
Figure 1: The histogram of salary of individual.

6DESCRIPTIVE STATISTICS
Reference
Chatfield, C. (2018). Statistics for technology: a course in applied statistics. Routledge.
Holcomb, Z. C. (2016). Fundamentals of descriptive statistics. Routledge.
Pyrczak, F. (2016). Success at statistics: A worktext with humor. Routledge.
Silverman, B. W. (2018). Density estimation for statistics and data analysis. Routledge.