MAT201 Mod 2

Module 2 - Case

Measures of Central Tendency and Variability

Assignment Overview

To complete this assignment, first review Chapter 2: Descriptive Statistics from the background reading using the OpenStax e-textbook. Please have special focus on the following sections:

2.3 Measures of the Location of the Data 2.5 Measures of the Center of the Data 2.6 Skewness and the Mean, Median, and Mode 2.7 Measures of the Spread of the Data

Note: By submitting this assignment, you affirm that it contains all original work, and that you are familiar with Trident University’s Academic Integrity policy in the Trident Policy Handbook. You affirm that you have not engaged in direct duplication, copy/pasting, sharing assignments, collaboration with others, contract cheating and/or obtaining answers online, paraphrasing, or submitting/facilitating the submission of prior work. Work found to be unoriginal and in violation of this policy is subject to consequences such as a failing grade on the assignment, a failing grade in the course, and/or elevated academic sanctions. You affirm that the assignment was completed individually, and all work presented is your own.

Assignment Expectations

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible. If the answer is in %, show two decimal places.

Answer the following problems showing your work and explaining (or analyzing) your results. Submit your work in a typed Microsoft Word document.

Below are excel functions, which you can use to solve for measures of central tendency and variability. You can use the formulas too; but, they will be time consuming.

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EXCEL FUNCTIONS

Measures of Central Tendency

Suppose data are in cells A1 to A10

Mean =AVERAGE(A1:A10)

Median =MEDIAN(A1:A10)

Mode =MODE(A1:A10)

Measures of Variability

Suppose data are in cells A1 to A10

Range =MAX(A1:A10)-MIN(A1:A10)

IQR =QUARTILE.EXC(Array,3)-QUARTILE.EXC(Array,1)

Population Variance σ2 =VAR.P(A1:A10)

Sample Variance s2 =VAR(A1:A10) or VAR.S(A1:A10)

Population Standard Deviation σ =STDEV.P(A1:A10)

Sample Standard Deviation s =STDEV(A1:A10) or STDEV.S(A1:A10)

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1. Joe and Mary would like to buy their first home in a new city. Below is the list of prices of 20 homes for sale.

   Prices in U.S. Dollars	140	190	265	115	270	240	250	180	160	201
   	240	280	175	200	310	195	320	105	385	264

   1. Find the mean, median, mode. (2 pts)
   2. Which measure of central tendency best represent the data? Why? (2 pts)
   3. Are there any outliers? If so, name the outlier. (2 pts)

1. The ages of students in a statistics class are listed below.

   Age of students	22	20	25	23	27	30	18	31	19	45
   	45	19	36	27	19	26	33	40	35	24

   1. Create a stem plot (2 pts)
   2. What is the mean age of the students? (2 pts)

1. Jenny likes to have at least a 70% average to pass her statistics class. Her previous four test scores are 52%, 66%, 76% and 71%. What is the minimum score Heidi needs on the final exam to pass the class? (4 pts)
   
2. Consider the following data and corresponding weights.

   Xi	Weight (wi )
   3.1	5
   2.3	3
   2.8	2
   4	4

   1. Compute the weighted mean. (2 pts)
   2. Compute the mean without weighting. (2 pts)
      
3. The chart below represents the amount of rainfall for 15 days in northern Ohio in July.

   Rainfall in inches

   4.1

   4.2

   3.5

   3.9

   4.2

   4.4

   3.8

   3.7

   3.3

   3.4

   4.3

   3.2

   4.6

   4.5

   4.0

   1. Complete the frequency table. (2 pts)

      Rainfall in inches	Frequency
      Less than 3.0
      3.0–3.4
      3.5–3.9
      4.0–4.5
      4.6–5.0

   2. Find the mean of the raw data. (2 pts)
   3. Find the median of the raw data. (2 pts)
   4. Find the mode of the raw data. (2 pts)
      
4. Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28 and 25.
   
   1. What is the minimum? (2 pts)
   2. What is the first quartile? (2 pts)
   3. What is the median? (2 pts)
   4. What is the third quartile? (2 pts)
   5. What is the maximum? (2 pts)
      
5. Create the box plot for the data in #6. Label the five points on the box. (4 pts)
   
6. Using the data in Question 6:
   1. What is the range? (2 pts)
   2. What is the interquartile range (IQR)? (2 pts)
      
7. The histogram of a quantitative variable is positively skewed. The mean of the variable is 35.
   1. Which one of the following is a more likely value of the median? (2 pts)
      
      55
      30
      35
   2. Support your answer. (2 pts)
      
8. A histogram of a given data shows three clear peaks. This may mean that (2 pts)
   1. There are three distinct groups in the data
   2. There are three modes in the data
   3. Both a and b are correct