# Chapter 1: An Introduction to Analyzing Statistical Data

Difficulty Level: Advanced Created by: CK-12

Chapter Outline

## Part One: Multiple Choice

1. Which of the following is true for any set of data?
1. The range is a resistant measure of spread.
2. The standard deviation is not resistant.
3. The standard deviation can be greater than the range.
4. The IQR\begin{align*}IQR\end{align*} is always greater than the range.
5. The range can be negative.
2. The following shows the mean number of days of precipitation by month in Juneau, Alaska in 2008:
Mean Number of Days With Precipitation > 0.1 inches
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
18 17 18 17 17 15 17 18 20 24 20 21

Which month contains the median number of days of rain?

(a) January

(b) February

(c) June

(d) July

(e) September

1. Given the data 2, 10, 14, 6, which of the following is equivalent to x¯¯¯\begin{align*}\overline{x}\end{align*}?
1. mode
2. median
3. midrange
4. range
5. none of these
2. Place the following in order from smallest to largest. I. Range\begin{align*}\text{I. Range}\end{align*} II. Standard Deviation\begin{align*}\text{II. Standard Deviation}\end{align*} III. Variance\begin{align*}\text{III. Variance}\end{align*}
1. I, II, III
2. I, III, II
3. II, III, I
4. II, I, III
5. It is not possible to determine the correct answer.
3. On the first day of school, a teacher asks her students to fill out a survey with their name, gender, age, and homeroom number. How many quantitative variables are there in this example?
1. 0
2. 1
3. 2
4. 3
5. 4
4. You collect data on the shoe sizes of the students in your school by recording the sizes of 50 randomly selected males’ shoes. What is the highest level of measurement that you have demonstrated?
1. nominal
2. ordinal
3. interval
4. ratio
5. According to a 2002 study, the mean height of Chinese men between the ages of 30 and 65 is 164.8 cm, with a standard deviation of 6.4 cm (http://aje.oxfordjournals.org/cgi/reprint/155/4/346.pdf accessed Feb 6, 2008). Which of the following statements is true based on this study?
1. The interquartile range is 12.8 cm.
2. All Chinese men are between 158.4 cm and 171.2 cm.
3. At least 75% of Chinese men between 30 and 65 are between 158.4 and 171.2 cm.
4. At least 75% of Chinese men between 30 and 65 are between 152 and 177.6 cm.
5. All Chinese men between 30 and 65 are between 152 and 177.6 cm.
6. Sampling error is best described as:
1. The unintentional mistakes a researcher makes when collecting information
2. The natural variation that is present when you do not get data from the entire population
3. A researcher intentionally asking a misleading question, hoping for a particular response
4. When a drug company does its own experiment that proves its medication is the best
5. When individuals in a sample answer a survey untruthfully
7. If the sum of the squared deviations for a sample of 20 individuals is 277, the standard deviation is closest to:
1. 3.82
2. 3.85
3. 13.72
4. 14.58
5. 191.82

## Part Two: Open-Ended Questions

1. Erica’s grades in her statistics classes are as follows: Quizzes: 62, 88, 82 Labs: 89, 96 Tests: 87, 99
1. In this class, quizzes count once, labs count twice as much as a quiz, and tests count three times as much as a quiz. Determine the following:
1. mode
2. mean
3. median
4. upper and lower quartiles
5. midrange
6. range
2. If Erica’s quiz grade of 62 was removed from the data, briefly describe (without recalculating) the anticipated effect on the statistics you calculated in part (a).
2. Mr. Crunchy’s sells small bags of potato chips that are advertised to contain 12 ounces of potato chips. To minimize complaints from their customers, the factory sets the machines to fill bags with an average weight of 13 ounces. For an experiment in his statistics class, Spud goes to 5 different stores, purchases 1 bag from each store, and then weighs the contents. The weights of the bags are: 13.18, 12.65, 12.87, 13.32, and 12.93 ounces.

(a) Calculate the sample mean.

(b) Complete the chart below to calculate the standard deviation of Spud’s sample.

Observed Data (xx¯¯¯)\begin{align*}(x-\overline{x})\end{align*} (xx¯¯¯)2\begin{align*}(x-\overline{x})^2\end{align*}
13.18
12.65
12.87
13.32
12.93
Sum of the squared deviations

(c) Calculate the variance.

(d) Calculate the standard deviation.

(e) Explain what the standard deviation means in the context of the problem.

1. The following table includes data on the number of square kilometers of the more substantial islands of the Galapagos Archipelago. (There are actually many more islands if you count all the small volcanic rock outcroppings as islands.)
Island Approximate Area (sq. km)
Baltra 8
Darwin 1.1
Española 60
Fernandina 642
Floreana 173
Genovesa 14
Isabela 4640
Marchena 130
North Seymour 1.9
Pinta 60
Pinzón 18
Rabida 4.9
San Cristóbal 558
Santa Cruz 986
Santa Fe 24
Santiago 585
South Plaza 0.13
Wolf 1.3

(a) Calculate each of the following for the above data:

(i) mode

(ii) mean

(iii) median

(iv) upper quartile

(v) lower quartile

(vi) range

(vii) standard deviation

(b) Explain why the mean is so much larger than the median in the context of this data.

(c) Explain why the standard deviation is so large.

1. At http://content.usatoday.com/sports/baseball/salaries/default.aspx, USA Today keeps a database of major league baseball salaries. Pick a team and look at the salary statistics for that team. Next to the average salary, you will see the median salary. If this site is not available, a web search will most likely locate similar data.

(a) Record the median and verify that it is correct by clicking on the team and looking at the salaries of the individual players.

(b) Find the other measures of center and record them.

(i) mean

(ii) mode

(iii) midrange

(iv) lower quartile

(v) upper quartile

(vi) IQR\begin{align*}IQR\end{align*}

(c) Explain the real-world meaning of each measure of center in the context of this data.

(i) mean

(ii) median

(iii) mode

(iv) midrange

(v) lower quartile

(vi) upper quartile

(vii) IQR\begin{align*}IQR\end{align*}

(d) Find the following measures of spread:

(i) range

(ii) standard deviation

(e) Explain the real-world meaning of each measure of spread in the context of this situation.

(i) range

(ii) standard deviation

(f) Write two sentences commenting on two interesting features about the way the salary data are distributed for this team.

Keywords

Bias

Bimodal

Categorical variable

Census

Chebyshev's Theorem

Deviation

Interquartile range (IQR)\begin{align*}(IQR)\end{align*}

Interval

Interval estimate

Levels of measurement

Lower quartile

Mean

Mean absolute deviation

Median

Midrange

Mode

n%\begin{align*}n\%\end{align*} trimmed mean

Nominal

Numerical variable

Ordinal

Outliers

Parameter

Percentile

Point estimate

Population

Qualitative variable

Quantitative variable

Range

Ratio

Resistant

Sample

Sampling error

Standard deviation

Statistic

Trimmed mean

Unit

Upper quartile

Variables

Variance

Weighted mean

Weighted mean

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Date Created:
Aug 20, 2013
Jan 14, 2016