Chapter 2 - Descriptive Statistics

Question 1

John Tukey

Answer 1

• 1915 - 2000
• exploratory data analysis (EDA) = boxplots, stem-and-leaf plots
• coined terms such as bit and software

Question 2

Features of a good numeric or graphic form of data submission

Answer 2

• self-contained
• understandable without reading the text
• clearly labeled of attributes with well-defined terms
• indicate principal trends in data

Question 3

Measures of location

Answer 3

• also known as measures of central tendency
• data summarization is important before any inferences can be made
• measure of location is useful for data summarization that defines the center or middle of the sample

Question 4

Arithmetic mean limitation

Answer 4

• oversensitive to extreme values

- in which case, it may not be representative of the location of the majority of sample points

Question 5

Symmetric distribution

Answer 5

arithmetic mean is approximately the same as the median

Question 6

Positively skewed distribution

Answer 6

• tail end is on the right side

- arithmetic mean tends to be larger than the median

Question 7

Negatively skewed distribution

Answer 7

• tail end is on the left side

- arithmetic mean tends to be smaller than the median

Question 8

Mode

Answer 8

• the most frequently occurring value among all the observations in a sample
• data distributions may have one or more modes (unimodal, bimodal, trimodal, etc.)

Question 9

Range

Answer 9

• the difference between the largest and smallest observations in a sample
• range is very sensitive to extreme observations or outliers
• larger the sample size n, the larger the range tends to be and the more difficult the comparison between ranges from data sets of varying sizes

Question 10

Quantiles or percentiles

Answer 10

• a better approach than range to quantifying the spread in data sets is percentiles or quantiles
• percentiles are less sensitive to outliers and are not greatly affected by the sample size

Question 11

Standard deviation

Answer 11

standard deviation is a reasonable measure of spread if the distribution is bell-shaped

Question 12

Grouped data

Answer 12

• when sample size is too large to display all the raw data, data are frequently collected in grouped form
• the simplest way to display the data is to generate a frequency distribution using a statistical package

Question 13

Frequency distribution

Answer 13

• frequency distribution = ordered display of each value in a data set together with its frequency
• if the number of unique sample values is large, then a frequency distribution may still be too detailed
• if the data is too large, then the data is categorized into broader groups

Question 14

Types of grouped data

Answer 14

• bar graphs
• stem and leaf plots
• box and whisker plot
• scatter plot
• histogram

Question 15

Bar graphs

Answer 15

• identity of the sample points within the respective groups is lost

Question 16

Stem and leaf plots

Answer 16

• easy to compute the median and other quantities
• each data point is converted into stem and leaf
• the collection of leaves indicates the shape of the data distribution

Question 17

Box and whisker plot

Answer 17

• uses the relationships among the median, upper quartile, and lower quartile to describe the skewness or symmetry of a distribution
• a vertical bar connects the upper quartile to the largest non-outlying value in the sample
• a vertical bar connects the lower quartile to the smallest non-outlying value in the sample

Question 18

Box and whisker plot (symmetric)

Answer 18

• upper and lower quartiles should be approximately equally spaced from the median

Question 19

Box and whisker plot (positively skewed)

Answer 19

• upper quartile is farther from the median than the lower quartile

Question 20

Box and whisker plot (negatively skewed)

Answer 20

• lower quartile is farther from the median than the upper quartile

Question 21

Box and whisker plot (outlying value)

Answer 21

• x > upper quartile + 1.5 IQR

- x < lower quartile - 1.5 IQR

Question 22

Box and whisker plot (extreme outlying value)

Answer 22

• x > upper quartile + 3.0 IQR

- x < lower quartile - 3.0 IQR