section 2.1: examining numerical data

Question 1

What is a scatterplot used for?

Answer 1

Visualizing the relationship between two numerical variables

Question 2

What does a dot plot visualize?

Answer 2

One numerical variable. Darker colors represent areas with more observations

Question 3

What does a stacked dot plot represent?

Answer 3

Higher bars indicate areas with more observations, aiding in judging the center and shape of the distribution

Question 4

What is the purpose of a histogram?

Answer 4

Provides a view of data density, showing where data is relatively more common

Question 5

What does the term ‘center’ refer to in statistics?

Answer 5

Mean or average of the distribution

Question 6

What is the formula for the sample mean?

Answer 6

x̄ = (x1 + x2 + x3 + … + xn) / n

Question 7

How is the population mean computed?

Answer 7

Computed the same way as sample mean, usually impossible to calculate due to lack of access to the entire population

Question 8

What does x̄ represent?

Answer 8

Sample mean

Question 9

What does μ represent?

Answer 9

Population mean

Question 10

Define unimodal

Answer 10

A distribution with a single peak

Question 11

What is the difference between bimodal and multimodal?

Answer 11

Bimodal has two peaks, while multimodal has several prominent peaks

Question 12

What characterizes a uniform distribution?

Answer 12

No apparent peaks

Question 13

What does ‘right skewed’ refer to?

Answer 13

A distribution with a tail extending to the right

Question 14

What does ‘left skewed’ mean?

Answer 14

A distribution with a tail extending to the left

Question 15

What is the formula for variance?

Answer 15

s^2 = (sum of(x - x̄)^2)/(n-1)

Question 16

How is standard deviation calculated?

Answer 16

s = √(s^2)

Question 17

What is the median in a dataset?

Answer 17

The value that splits the data in half when ordered in ascending order

Question 18

What does Q1 represent?

Answer 18

25th percentile, also called the first quartile

Question 19

What is the 50th percentile also known as?

Answer 19

The median

Question 20

What does Q3 represent?

Answer 20

75th percentile, also called the third quartile

Question 21

Define interquartile range (IQR)

Answer 21

The range where the middle 50% of the data lies, calculated as IQR = Q3 - Q1

Question 22

What is the maximum upper whisker reach?

Answer 22

Q3 + 1.5 x IQR

Question 23

What is the maximum lower whisker reach?

Answer 23

Q1 - 1.5 x IQR

Question 24

Define an outlier

Answer 24

An observation beyond the maximum reach of the whiskers

Question 25

What are robust statistics?

Answer 25

Median and IQR

Question 26

What are not robust statistics?

Answer 26

Mean, variance (standard deviation)

Question 27

When describing distributions, what three aspects do we focus on?

Answer 27

Center, shape, and spread of distributions

Question 28

Which plots are used for 2-numerical variable distributions?

Answer 28

Scatter plot

Question 29

Which plots are used for 1-numerical variable distributions?

Answer 29

Dot plot, stacked dot plot, histogram, box plot

Question 30

Why are histograms important?

Answer 30

They are the most important distributions for analysis

Question 31

How can the chosen bin width affect a histogram?

Answer 31

It can alter the story the histogram is telling

Question 32

What does the median represent in relation to data values?

Answer 32

50% of the values are below it and 50% are above

Question 33

What are ways to measure center?

Answer 33

* Histograms * Mean (average) * Median

Question 34

What are ways to measure shape?

Answer 34

* Modality * Skewness

Question 35

What are ways to measure spread?

Answer 35

* Variance (standard deviation) * IQR

Question 36

For skewed distributions, which measures are more helpful?

Answer 36

Median and IQR to describe center and spread

Question 37

For symmetric distributions, which measures are more helpful?

Answer 37

Mean and SD to describe center and spread

Question 38

Which variable is expected to be uniformly distributed: (a) heights of KSU students, (b) salaries of a random sample of people from North Carolina, (c) house prices in America, (d) birthdays of classmates (day of the month)?

Answer 38

(d) Birthdays of classmates (day of the month)

Question 39

Why is it important to look for outliers?

Answer 39

* Identify extreme skew in the distribution * Identify data collection and entry errors * Provide insight into interesting features of the data

Question 40

How would replacing the largest value with $10 million affect the mean, median, standard deviation, and IQR of household income?

Answer 40

* Mean: increase * Median: may not change much * Standard deviation (variance): increase * IQR: stay the same

Question 41

If the smallest value in household income is replaced with $10 million, how does it affect the mean and median?

Answer 41

* Mean: increase * Median: stay the same or not change by much

Question 42

For estimating typical household income for a student, is the mean or median more relevant?

Answer 42

The median, because the distribution is skewed