15 - Data Summarization and Visualization

Question 1

What does descriptive statistics refer to?

Answer 1

Methods for summarizing and organizing the information in a data set.

Question 2

What are elements in a data set?

Answer 2

Entities for which information is collected.

Question 3

What is a variable?

Answer 3

A characteristic of an element, which takes on different values for different elements.

Question 4

What are observations in a data set?

Answer 4

The set of variable values for a particular element.

Question 5

What are qualitative variables?

Answer 5

Variables that enable the elements to be classified or categorized according to some characteristic.

Question 6

What are quantitative variables?

Answer 6

Variables that take numeric values and allow arithmetic to be meaningfully performed on them.

Question 7

What are the four levels of measurement for data?

Answer 7

• Nominal * Ordinal * Interval * Ratio

Question 8

What is nominal data?

Answer 8

Data that refer to names, labels, or categories without natural ordering.

Question 9

What is ordinal data?

Answer 9

Data that can be rendered into a particular order but cannot have arithmetic meaningfully performed on them.

Question 10

What is interval data?

Answer 10

Quantitative data defined on an interval without a natural zero where addition and subtraction may be performed.

Question 11

What is ratio data?

Answer 11

Quantitative data for which all arithmetic operations may be performed and a natural zero exists.

Question 12

What is a discrete variable?

Answer 12

A numerical variable that can take either a finite or a countable number of values.

Question 13

What is a continuous variable?

Answer 13

A numerical variable that can take infinitely many values, forming an interval on the number line.

Question 14

What is a population in statistics?

Answer 14

The set of all elements of interest for a particular problem.

Question 15

What is a parameter?

Answer 15

A characteristic of a population, usually unknown but constant.

Question 16

What is a sample?

Answer 16

A subset of the population.

Question 17

What is a statistic?

Answer 17

A characteristic of a sample.

Question 18

What is a census?

Answer 18

The collection of information from every element in the population.

Question 19

What does statistical inference refer to?

Answer 19

Methods for estimating or drawing conclusions about population characteristics based on a sample.

Question 20

What is a random sample?

Answer 20

A sample for which each element has an equal chance of being selected.

Question 21

What is a predictor variable?

Answer 21

A variable whose value is used to help predict the value of the response variable.

Question 22

What is a response variable?

Answer 22

A variable of interest whose value is presumably determined by the predictor variables.

Question 23

What does frequency refer to in categorical data?

Answer 23

The number of data values in each category.

Question 24

What is a relative frequency?

Answer 24

The frequency of a category divided by the number of cases.

Question 25

What is a frequency distribution?

Answer 25

A distribution consisting of all categories that the variable assumes, together with their frequencies.

Question 26

What is a bar chart?

Answer 26

A graph used to represent the frequencies or relative frequencies for a categorical variable.

Question 27

What is a Pareto chart?

Answer 27

A bar chart where the bars are arranged in decreasing order.

Question 28

What is a pie chart?

Answer 28

A circle divided into slices, with the size of each slice proportional to the relative frequency of the category.

Question 29

How are quantitative data grouped?

Answer 29

Into classes, with lower and upper limits defining the classes.

Question 30

What is a cumulative frequency distribution?

Answer 30

A distribution showing the total number of data values less than or equal to the upper class limit.

Question 31

What is a histogram?

Answer 31

A graphical representation of a frequency distribution for a quantitative variable.

Question 32

What is a stem-and-leaf display?

Answer 32

A display showing the shape of the data distribution while retaining the original data values.

Question 33

What is a dotplot?

Answer 33

A plot where each dot represents one or more data values set above the number line.

Question 34

What is a symmetric distribution?

Answer 34

A distribution that can be split into two halves that are approximately mirror images of each other.

Question 35

What characterizes right-skewed data?

Answer 35

A longer tail on the right than the left.

Question 36

What characterizes left-skewed data?

Answer 36

A longer tail on the left than the right.

Question 37

What does the summation notation ∑x mean?

Answer 37

To add up all the data values x.

Question 38

What are measures of center?

Answer 38

* Mean * Median * Mode * Midrange

Question 39

How is the mean calculated?

Answer 39

Add up the values and divide by the number of values.

Question 40

What is the median?

Answer 40

The middle data value when sorted in ascending order.

Question 41

What is the mode?

Answer 41

The data value that occurs with the greatest frequency.

Question 42

What is the midrange?

Answer 42

The average of the maximum and minimum values in a data set.

Question 43

How does skewness affect the mean and median?

Answer 43

For symmetric data, they are approximately equal; for right-skewed, mean > median; for left-skewed, median > mean.

Question 44

What are measures of variability?

Answer 44

* Range * Variance * Standard deviation * Interquartile range (IQR)

Question 45

How is the range calculated?

Answer 45

Difference between the maximum and minimum values.

Question 46

What is the relationship between the mean and median in right-skewed data?

Answer 46

The mean is greater than the median.

Question 47

What is the relationship between the mean and median in left-skewed data?

Answer 47

The median is greater than the mean.

Question 48

What are the measures of variability that quantify the amount of variation in data?

Answer 48

* Range * Variance * Standard deviation * Interquartile range (IQR)

Question 49

How is the range of a variable calculated?

Answer 49

Range = max(value) - min(value).

Question 50

What is a deviation in the context of data analysis?

Answer 50

The signed difference between a data value and the mean value.

Question 51

What is the formula for population variance?

Answer 51

σ² = (Σ(x - μ)²) / N

Question 52

What is the square root of the population variance called?

Answer 52

Population standard deviation.

Question 53

What is the difference between sample variance and population variance?

Answer 53

Sample variance uses n - 1 in the denominator to be an unbiased estimator.

Question 54

What is the formula for sample standard deviation?

Answer 54

s = √(s²)

Question 55

Why is standard deviation preferred over variance for reporting results?

Answer 55

Standard deviation is expressed in the original units.

Question 56

What does the sample standard deviation represent?

Answer 56

The size of the typical deviation from the mean.

Question 57

What is the definition of the pth percentile in a data set?

Answer 57

The data value such that p percent of the values are at or below this value.

Question 58

What is the percentile rank of a data value?

Answer 58

The percentage of values in the data set that are at or below that value.

Question 59

How is the Z-score calculated?

Answer 59

Z-score = (x - μ) / s

Question 60

What does a Z-score represent?

Answer 60

How many standard deviations a data value lies above or below the mean.

Question 61

What does the Empirical Rule state for a normal distribution?

Answer 61

* About 68% of data within one standard deviation * About 95% of data within two standard deviations * About 99.7% of data within three standard deviations

Question 62

What is the first quartile (Q1) in a data set?

Answer 62

The 25th percentile of the data set.

Question 63

What is the formula for calculating the interquartile range (IQR)?

Answer 63

IQR = Q3 - Q1

Question 64

How is an outlier defined using the IQR method?

Answer 64

* x ≤ Q1 - 1.5(IQR) * x ≥ Q3 + 1.5(IQR)

Question 65

What does the five-number summary of a data set consist of?

Answer 65

* Minimum * Q1 * Median * Q3 * Maximum

Question 66

What is a boxplot used for?

Answer 66

To recognize symmetry and skewness in a data distribution.

Question 67

What does the left whisker in a boxplot indicate?

Answer 67

The minimum value that is not an outlier.

Question 68

What characterizes a left-skewed distribution in a boxplot?

Answer 68

The left whisker is longer than the right whisker.

Question 69

What is a bivariate relationship?

Answer 69

The relationship between two variables.

Question 70

What is a contingency table?

Answer 70

A crosstabulation of two categorical variables.

Question 71

What does a clustered bar chart represent?

Answer 71

A graphical representation of a contingency table.

Question 72

How can we summarize the relationship between a quantitative variable and a categorical variable?

Answer 72

By calculating summary statistics for the quantitative variable for each level of the categorical variable.

Question 73

What is an individual value plot?

Answer 73

A set of vertical dotplots for each category in a categorical variable.

Question 74

What is a scatter plot used for?

Answer 74

To visualize the relationship between two quantitative variables.

Question 75

What does the correlation coefficient r indicate?

Answer 75

The strength and direction of the linear relationship between two quantitative variables.

Question 76

What are the possible values of the correlation coefficient r?

Answer 76

−1 ≤ r ≤ 1.

Question 77

What does a positive and significant r indicate?

Answer 77

x and y are positively correlated.

Question 78

What does a negative and significant r indicate?

Answer 78

x and y are negatively correlated.