Discuss the importance of the Measures of Variation.

Deliverable 01 Worksheet

- Introduce your scenario and data set.

· Provide a brief overview of the scenario you are given and describe the data set.

· Describe how you will be analyzing the data set.

· 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, ratio).

Answer and Explanation:

The scenario is about the client who is interested in finding out the salary distributions of jobs in the Minnesota state that range from $30,000 to $200,000 per year. The data set provided in the scenario consists of 364 records from the Bureau of Labor Statistics and contain a listing of titles of several jobs with yearly salaries in $30,000 to $200,000 range.

I will be analyzing the data set using the descriptive statistics which is a quantitative data analysis method. This will help me to summarize the data and find patterns in the salaries.

The salaries are quantitative variables, while Job titles are qualitative variables. Salary being a quantitative variable, it is also discrete.

The salary variable is in an ordinal level of measurement since the salary values depict some ordered relationship. Job title variable is a normal level of measurement as it is used only to classify the data.

- Discuss the importance of the Measures of Center.

· Name and describe each measure of center.

· Discuss the advantages and/or disadvantages of each.

Answer and Explanation:

Mean: is the numerical average of a set of values, which is obtained by dividing the sum of all values by the number of the values. It is the best measure of central tendency as it takes into account all values. It is also useful when comparing sets of data.

However, mean is affected easily by any extreme value; hence it is not the best measure to use in skewed distribution.

Median: it is the midpoint of a set of numerical values when arranged in order. It is not affected strongly by the extreme values or skewed data as the way mean is affected. It is the best measure to use in a skewed distribution. It is also useful in comparing sets of data and yields one distinct answer.

However, median is not used often as the way mean does.

Mode: it is the most common value among a set of values. It is useful in nominal data set in which both mode and median are undefined. It works with both numerical and non-numerical data. It is also useful in non-numerical data. It is not affected by outliers.

However, there may be more than one mode in a data set or even no mode at all in the data set. The mode tends to be useless if no values in the set repeat.

- Discuss the importance of the Measures of Variation.

· Name and describe each measure of variation.

· Discuss the advantages and/or disadvantages of each.

Answer and Explanation:

Range: it is the highest score minus the lowest score. It is the simplest measure of variability to calculate and can be used as a measure of variability where precision is not required. However, the value of range is affected by two extreme values only. Also, range is not stabling from sample to sample. It is not sensitive to the distribution’s total condition. The range depends on the sample size, it tends to be greater when the sample size is greater.

Inter-quartile range: it is the range of the middle 50% of the values in a distribution. It is less sensitive to the outliers. It is not amenable to mathematical manipulation. It is a good measure of variation when the distribution is skewed. However, its sampling stability is not up to the standard deviation.

Variance: it is the measure of the dispersion of a set of data around the value of their mean. It defines how close the values in the distribution are to the middle of the distribution. It is equal to the sum of squared differences between the observed values and their mean, divided by the total number of the observations. It is a common measure of data dispersion. The figures obtained in variance are large, and hard to compare since the unit of measurement is squared.

Standard deviation: it is the square root of the variance. It is a useful measure of variability when the distribution is normal or approximately normal, since the proportion of the distribution within a given number of standard deviations from the mean can be calculated. It is most common measure of variability for a single data set. It is resistant to sampling variation, and it is commonly used in both inferential and descriptive statistics. However, it is responsive to exact position of each score in the distribution. It is more sensitive than inter-quartile range to the presence of few extreme scores in the distribution.

Coefficient of variation: it is equal to the standard deviation divided by the mean of the data set. It is also referred to as a relative standard deviation. It is useful in comparing two data sets unlike standard deviation. Its actual value is independent of the unit in which the measurement has been taken; hence it is a dimensionless number. However, the value of coefficient of variation approaches to infinity when the average value is zero; hence it is quite sensitive to small changes in mean values. It cannot be directly used to construct confidence intervals for the mean.

- 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 context of the scenario (for example, if the median is larger than the mean, what does it mean? What does the value of standard deviation tell you?) and (b) correct units of measurement. Show your calculations in your spreadsheet. You do not need to include Excel functions in your written answer below.

· Mean

· Median

· Mode

· Midrange

· Range

· Variance

· Standard deviation

Answer and Explanation:

From the calculations of the measures of center and measures of variation from the scenario data set, the following are the respective answers.

- Mean = 71,879 dollars
- Median = 66,525 dollars
- Mode = 71,420 dollars
- Midrange = 116,100 dollars
- Range=167,760 dollars
- Variance = 546,033,522 dollars^2
- Standard deviation =23,367.36018 dollars

Explanation:

The mean value means that the most common salary of jobs in the state of Minnesota is 71,879 dollars. Also, it can be observed that the mean is greater than the median, hence this means that the distribution of the salary of jobs in the state of Minnesota is skewed to the right, thus bunched up toward the left and with a tail stretching toward the right. The standard deviation obtained in the scenario is high, hence indicates that the salary of jobs in the state of Minnesota are spread out over a large range of values.

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