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Running head: DESCRIPTIVE STATISTICS

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Descriptive statistics
Name
Institution
Date

DESCRIPTIVE STATISTICS

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Deliverable 01 Worksheet
1. Introduce your scenario and data set.
o Provide a brief overview of the scenario you are given and describe the data set.
o Describe how you will be analyzing the data set.
o Classify the variables in your data set.
▪ Which variables are quantitative/qualitative?
▪ If it is a quantitative variable, is it discrete or continuous?
▪ Describe the level of measurement for each variable included in the data set
(nominal, ordinal, interval, and ratio).
Answer and Explanation:

The discussion revolves around a data set of 364 observations of salaries for various jobs in
the state of Minnesota. The discussion aims at presenting a descriptive analysis of the salary
distribution. The data set comprises two variables; Job title and Salary (in dollars) for each job
title. The Job title is a qualitative variable assuming nominal scales since the names are merely
for identification and classification. The salary amount is a quantitative and continuous variable
since the values are given in numerical values. The variable assumes a ratio scale of
measurement since zero implies absence of the quantity.

2. Discuss the importance of the Measures of Center.
o Name and describe each measure of center.
o Discuss the advantages and/or disadvantages of each.
Answer and Explanation:
The measures of center are summary statistics that reveal the center point of the data
or the typical value. They include the mean, median, and mode. The mean reveals the center
by presenting the most typical value for a given data. It is evaluated by summing up all the
values in a data set and dividing by the total count of the observation. The advantage of
using the mean is that it includes all the values in its calculation and its calculations are
simple. The disadvantage of using mean is that it may not accurately represent the center of
data that is skewed or that which contains outliers.
The median reveals the center of data by presenting the middle-most value in a
group of data arranged in ascending order. The advantage of the median is that is not
affected by outliers or skewed data and as such, it is more appropriate for skewed
distributions. The disadvantage of using the mean is that it does not account for all the
values in the data set, thereby, disregarding the precise value of each observation.

DESCRIPTIVE STATISTICS

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The mode presents the most occurring or the most common value in a group of data.
The mode of more appropriate for categorical, discrete, and ordinal data. The disadvantage
of using the mode is that it is ill-defined for continuous data and does not include all values
in its calculation.
3. Discuss the importance of the Measures of Variation.
o Name and describe each measure of variation.
o Discuss the advantages and/or disadvantages of each.
Answer and Explanation:
The measures of variations reveal the spread or the dispersion of data. They include
the variance, range, and standard deviation. The range indicates spread by revealing the
difference between the smallest and largest values. The advantage of using the range is that
it is easy to compute and understand. The demerits of using the range are that it dependents
on the two most extreme values and as such, affected by any fluctuations. Additionally, it’s
not a reliable measure of variation since it’s reliant on change of scale.
Variance describes the expectation or average of the squared deviation of the data
elements and the mean. The advantage of using variance is that it accounts for all deviations
from mean regardless of their direction. However, the disadvantage is that it gives more
weight to the outliers which could skew the results.
The standard deviation indicates spread by revealing the average distance between
the data values and the mean. It’s the square root of variance. The advantage of using the
standard deviation is that it ignores the direction of the mean deviations, hardly affected by
the changes in the observations, and is unaffected by changes in origin. The demerits are
that it’s complex to compute and understand in layman terms.

4. Calculate the measures of center and measures of variation from the data set and list them
below. Be sure to include (a) an interpretation of each measure in the conte...