Chapter 3 & 4

Question 1

Name the displays/tables that represent quantitative data.

Answer 1

Stem and Leaf Display, Dotplots, and Histogram which is a Frequency Distribution Table.

Question 2

Describe Dotplots Displays.

Answer 2

This plot was taken guessing the instructors age.

Question 3

Name a general rule and difference between historgrams and others (Stem and Leaf plots and Dotplots).

Answer 3

General Rule: Historgrams are used for large data sets. Stem and Leaf Display and Dotplots are used for smaller data sets. Differences: Historgrams do not display raw data but displays frequency (counts). The “others” show raw data and frequency.

Question 4

Name a general rule and difference between histograms and others (Stem and Leaf plots and Dotplots).

Answer 4

General Rule: Histograms are used for large data sets. Stem and Leaf Display and Dotplots are used for smaller data sets. Differences: Histograms do not display raw data but displays frequency (counts). The “others” show raw data and frequency.

Question 5

Name a major difference between bar charts and histograms.

Answer 5

Bar charts have a required distance between each bar, whereas histograms do not have any space between each bar.

Question 6

Humps in a histogram are called what?

Answer 6

Modes. Unimodal - one main peak Bimodal - two main peaks Multimodal -three or more peaks

Question 7

A histogram is ___________ if you fold it along a vertical line through the middle and have edges match closely.

Answer 7

symmetric.

Question 8

This describes how data are distributed.

Answer 8

shape of the data.

Question 9

What measures shape of a distribution?

Answer 9

Skewness.

Question 10

Here are 3 different shapes, name them in reference to skewness and symmetry.

Answer 10

1. Left-Skewed 2. Symmetric 3. Right-Skewed

Question 11

What are some standard notations used to describe distributions (histograms) numberically.

Answer 11

Mean, Standard Deviation, Variance, and Size.

Question 12

Name the numerical data properties?

Answer 12

Central Tendency, Variation (Dispersion) and Shape. Central Tendency tells you where the middle is. Variation tells you how spread is the data.

Question 13

What two tools measures of Central Tendency?

Answer 13

Mean and median.

Question 14

Describe how the median is found.

Answer 14

Order the data from smallest to largest. If odd n, then middle value of sequence. If even n, then average of 2 middle values.

Question 15

What 4 tools are used to measure variation.

Answer 15

Range, Interquartile Range, Variance, Standard Deviation.

Question 16

This is a measure of noncentral tendency and splits ordered data into 4 quarters. What is it?

Answer 16

Quartiles.

Question 17

Describe the method for finding quartiles.

Answer 17

If n is odd, the middle data is Q2. Then average the first two and final two for Q1 and Q3 respectfully. If n is even, average the two middle data for Q1. Split the entire data in half then the two middle data in each half for Q1 and Q3.

Question 18

Describe how the interquartile range is found.

Answer 18

After finding the quartiles, Interquartile = Q3 - Q1.

Question 19

This is a measure of dispersion, ignores how the data are distributed and is the difference between largest and smallest observations.

Answer 19

The Range.

Question 20

These are measures of dispersion, the most common measures, considered how data are distributed and show variation about the mean.

Answer 20

Standard deviation and variance.

Question 21

Sample variance defintional formula.

Answer 21

S² = Σ(Y_i - Y_avg.)²/(n-1)

Question 22

Measures the average squared distance that all the observations are from the mean.

Answer 22

The variance.

Question 23

Sample Standard Deviation Formula.

Answer 23

S = (S²)^1/2

Question 24

Why is the standard deviation preferred over the variance?

Answer 24

The units of the variance are squared and could be misleading, where the standard deviation will hold proper units.

Question 25

Variance Computational Formula.

Answer 25

s² = (Σy² - ((Σy)²/n)) / (n-1)

Question 26

A \_-\_\_\_\_\_\_ _________ consists of the median, the quartiles, and the extremes of the data.

Answer 26

5-number summary.

Question 27

What is a box plot?

Answer 27

A graphical display of data using 5-number summary.

Question 28

Given these boxplots, determine the shape to the approiate boxplot.

Answer 28

From left to right: Left-Skewed, Symmetric, Right-Skewed.

Question 29

When you describe a distribution, you should always start by talking about three things. What are they?

Answer 29

Shape, center, and spread.

Question 30

The bins, together with these counts, give the _____________ of the quantitative variable and provide the building blocks for the display of the distribution, called a \_\_\_\_\_\_\_.

Answer 30

distribution, histogram.

Question 31

In terms of central tendency and the existence of outliers, which a better tool to use the median or the mean? Why?

Answer 31

Median. It is not affected by outliers, the mean is.

Question 32

In terms of variation and extreme values (which can present skewness), which is a better tool; range or I.Q.R.? Why?

Answer 32

I.Q.R., it is not effected by extreme values (outliers) or skewness. Range can be used when the spread (variation) is not effected by outliers.

Question 33

Like the mean, the _______ \_\_\_\_\_\_\_\_\_\_ is appropriate only for symmetric data. One way to think about spread is to examine how far each data value is from the mean. The difference is call a \_\_\_\_\_\_\_\_\_\_.

Answer 33

standard deviaton, deviation.

Question 34

Always pair the _______ with the IQR and the ______ with the standard deviation.

Answer 34

median, mean.

Question 35

An outlier is an extreme value that differs greatly from other values in a set of values. As a "rule of thumb", an extreme value is considered to be an outlier if it is at least ___ interquartile ranges below the first quartile (Q1), or at least ___ interquartile ranges above the third quartile (Q3).

Answer 35

1.5 Supremum = 1.5(IQR) + Q₃. Infimum = Q1 - 1.5(IQR). Therefore the outliers will be greater than the supremum and less than the infimum.