MODULE 1 - DESCRIPTIVE STATISTICS

Question 1

The study of statistics is often broken into what two main categories?

Answer 1

1. descriptive statistics
2. inferential statistics

Question 2

inferential statistics (3)

Answer 2

1. Frequently, it is impossible to contact every person in large populations, so a smaller group is used, called a sample.
2. A researcher can draw conclusions about the larger population using the sample data.
3. Focuses on using information from the sample to make conclusions about the population from which the sample was drawn.

Question 3

descriptive statistics (4)

Answer 3

1. focuses on summarizing survey data about a sample drawn from a population.
2. Summary statistics include measures of central tendency such as mean, median, and mode; and dispersion such as range and standard deviation.
3. Descriptive statistics cannot make conclusions based on the data. 4. Rather, descriptive statistics is a way to present data in a meaningful way.

Question 4

What is data?

Answer 4

is information, especially facts or numbers, usually collected or computed for purposes of analysis.

Question 5

Common sources of data (3)

Answer 5

1. Social networks
2. Traditional Business Systems
3. Internet of Things

Question 6

Data analytics

Answer 6

is the field of analyzing data to gain insight, draw conclusions, or make decisions.

Question 7

Big data

Answer 7

refers to very large data sets that cannot be processed by traditional methods, and is characterized by high volume, rapid velocity of collection, and variety in type and quality.

Question 8

3 Types of data analytics

Answer 8

1. Descriptive
2. Predictive
3. Prescriptive

Question 9

Descriptive data analytics

Answer 9

analytics seeks to describe data, providing insight and knowledge.

Question 10

Predictive data analytics

Answer 10

seeks to make predictions from data

Question 11

Prescriptive data analytics

Answer 11

seeks to make decisions (prescriptions) based on data

Question 12

Data is typically represented using what?

Answer 12

variables

Question 13

variable

Answer 13

is an item that can have different (“varying”) values

Question 14

Variables are often considered as being of two possible types:

Answer 14

1. quantitative variable
2. categorical variable

Question 15

quantitative variable

Answer 15

can take on a numeric value (quantitative data) that can be measured and ordered

Question 16

categorical variable (qualitative variable)

Answer 16

can take on the value (usually a label) of one of several categories

Question 17

reason for distinguishing variable types (3)

Answer 17

1. Each type is handled differently in data analytics
2. A categorical variable typically involves counting the instances of each category, often then depicted with a bar chart or pie chart.
3. But a quantitative variable is commonly plotted versus another quantitative variable, often depicted with a scatter plot or line chart

Question 18

Two types of categorical variables are often distinguished

Answer 18

1. Nominal
2. Ordinal

Question 19

Nominal variable

Answer 19

have no ordering, existing in name only, like apples, oranges, and grapes. (“Nominal” means “in name only”).

Question 20

Ordinal Variable

Answer 20

have an ordering, like disagree, neutral, and agree.

Question 21

Two types of quantitative variables are often distinguished

Answer 21

1. continuous variable
2. discrete variable

Question 22

continuous variable

Answer 22

are infinite along a continuum of values within a range, typically real numbers. Continuous variables usually represent measurements, like height ( meters) or temperature ( degrees).

Question 23

discrete variable (3)

Answer 23

1. are finite within a range, typically integers.
2. Discrete variables usually represent countable items, like people in a family () or cars in a city ().
3. Generally, if “number of” can be added to the beginning, the variable is discrete, like “number of people in a family”, but not “number of height”.

Question 24

Data visualization

Answer 24

is the display of data in a format, such as a table or chart, that seeks to achieve a goal of conveying particular information to a viewer

Question 25

Considerations for data visualization

Answer 25

1. Cardinality 2. depends on the kind of data being presented, and the information to be conveyed.

Question 26

Cardinality (2)

Answer 26

1. is the number of unique elements in a dataset. 2. scatter graphs, line charts, and histograms, work very well for high-cardinality data

Question 27

Pie charts

Answer 27

are a good choice for low-cardinality data, and for showing the relative frequency in which unrelated categories occur.

Question 28

scatter plot

Answer 28

can be used to identify trends.

Question 29

A bar chart

Answer 29

is a good choice for displaying frequency or counts in low-cardinality data.

Question 30

spreadsheet application

Answer 30

is a common computer application for organizing data like text or numbers, for using formulas to calculate a mathematical quantity using existing data as inputs, and for creating charts to visualize data.

Question 31

A spreadsheet consists of? (2)

Answer 31

1. A spreadsheet consists of cells organized into columns and rows. The column headings are letters and the row headings are numbers, but headings are not counted as cells. 2. A user can enter data, like words or numbers, into each cell. The spreadsheet is a convenient way to create a table of data.

Question 32

spreadsheet function

Answer 32

is a predefined formula that supports common tasks such as computing the average, minimum, or maximum of a group of cells.

Question 33

function syntax

Answer 33

defines how the function is used, and specifies the function's name and accepted arguments

Question 34

Function's arguments (3)

Answer 34

1. are surrounded by parentheses and specify the data that the function operates on. 2. Arguments may be numbers, cells, a range of cells, or a combination thereof. 3. The [ ] arguments are optional.

Question 35

To call a function in a spreadsheet

Answer 35

= is followed by the function's name and then arguments separated by commas.

Question 36

range operator (:)

Answer 36

1. defines a reference to a group of cells. 2. Ex: =SUM(A1:A4, B10) calculates the sum of cells A1, A2, A3, A4, and B10.

Question 37

The two primary methods of inferential statistics

Answer 37

confidence intervals, and hypothesis testing

Question 38

Confidence Intervals

Answer 38

specify the range within which a parameter falls with a given probability

Question 39

hypothesis testing

Answer 39

allows differences between population parameters to be compared.

Question 40

Surveys

Answer 40

Are conducted to allow statisticians to make generalizations about a population.

Question 41

population

Answer 41

is any collection of objects, people, or things about which statistical inference are made

Question 42

parameter of a population

Answer 42

is a numerical characteristic of a population, such as mean, median, or standard deviation.

Question 43

sampling unit

Answer 43

is an individual in the population on which a measurement can be taken.

Question 44

sampling frame

Answer 44

is the subset of the population from which a sample is drawn.

Question 45

sample

Answer 45

is composed of the sampling units that provide data to be collected.

Question 46

statistic

Answer 46

is a numerical characteristic of a sample, rather than the population.

Question 47

bias

Answer 47

is a difference between the parameter predicted from a survey from the true value of the parameter in the population.

Question 48

Two broad categories of statistical bias include

Answer 48

selection bias and response bias.

Question 49

selection bias

Answer 49

exists when the sampling units selected from a population are not representative of the entire population, and are instead biased toward certain subsets of the population.

Question 50

types of selection bias (4)

Answer 50

1. Undercoverage bias 2. Nonresponse bias 3. Voluntary response bias 4. Response bias

Question 51

Undercoverage

Answer 51

occurs when certain members of a population are inadequately represented in a sample.

Question 52

Nonresponse bias

Answer 52

occurs when a sample is biased toward members of a population that participate in a survey.

Question 53

Voluntary response bias

Answer 53

occurs when a sample is biased toward members that self-select for participation in a survey.

Question 54

response bias

Answer 54

can result if the responses of survey participants are affected by how a question is asked or the behaviors or attitudes of the participant.

Question 55

3 types of response bias

Answer 55

1. Acquiescence bias 2. extreme responding 3. social desirability bias

Question 56

Acquiescence bias

Answer 56

occurs when respondents tend to agree with a statement in a survey.

Question 57

extreme responding

Answer 57

occurs when respondents tend to select the most extreme options available.

Question 58

social desirability bias (2)

Answer 58

1. occurs when respondents tend to answer questions in a way that is socially accepted by others. 2. In other words, a social desirability bias exists when respondents over-report "good" behaviors or under-report "bad" behaviors.

Question 59

Sampling methods

Answer 59

Different sampling methods can help mitigate certain types of statistical bias.

Question 60

Types of sampling methods (5)

Answer 60

1. simple random sampling 2. systematic sampling 3. stratified 4. cluster 5. convenience

Question 61

simple random sampling (2)

Answer 61

1. a sample is constructed by random selection from the population. 2. Mathematically, simple random sampling is a sampling method in which all possible samples consisting of units selected from a population of units are equally likely.

Question 62

systematic sampling

Answer 62

every Kth unit from a population of units is selected to be in a sample.

Question 63

stratified sampling

Answer 63

the population is first divided into groups, or strata, depending on some characteristic. Next, samples within each stratum are randomly selected in a proportional manner.

Question 64

cluster sampling

Answer 64

1. the population is first divided into groups, or clusters, depending on some characteristic. 2. Next, the sample is constructed by randomly selecting one or more clusters.

Question 65

convenience sampling

Answer 65

units are drawn from a subset of the population that is readily available.

Question 66

outlier

Answer 66

a data value that is either much greater than or much less than the rest of the data and not representative of the rest of the data being considered

Question 67

Spread (3)

Answer 67

1. is a measure of how far apart values in a dataset are to each other 2. a larger spread means that the values are more scattered. 3. A lower spread means that the values are more clustered together.

Question 68

Graphical techniques include (3)

Answer 68

using dot plots, box plots, and histograms

Question 69

numerical techniques include calculating (3)

Answer 69

the interquartile range, variance, and standard deviation.

Question 70

Two common numerical measures of spread are

Answer 70

variance and standard deviation

Question 71

Variance

Answer 71

is the average of the square difference from the mean

Question 72

Standard deviation

Answer 72

is the square root of the variance

Question 73

The calculations for the variance and standard deviation depend on whether

Answer 73

the dataset contains the whole population or a subset of the population.

Question 74

What does the standard deviation represent?

Answer 74

The typical difference between a data value and the mean

Question 75

What does the range represent?

Answer 75

The spread between the maximum and minimum data values

Question 76

Which is a better measure of spread for the dataset represented in the computer output?

Answer 76

For symmetric data, standard deviation is usually the better measure of spread. For data that is skewed, interquartile range is usually the better measure of spread.

Question 77

maximum of a dataset

Answer 77

is the largest value in the dataset

Question 78

minimum of a dataset

Answer 78

is the smallest value in the dataset.

Question 79

range of a dataset

Answer 79

is the difference between the maximum and minimum of the dataset.

Question 80

percentile of a dataset

Answer 80

is the data value such that percent of the data falls at or below that value.

Question 81

first quartile (Q1) (2)

Answer 81

1. is the 25th percentile. One-quarter of the data fall at or below . 2. The first quartile is the median of the lower half of the data.

Question 82

third quartile (Q3) (3)

Answer 82

1. is the 75th percentile. 2. Three-quarters of the data fall at or below . 3. The third quartile is the median of the upper half of the data.

Question 83

50th percentile of a dataset.

Answer 83

Because half of the data fall at or below the median, the median is also the 50th percentile of a dataset.

Question 84

Collectively, the minimum and maximum values, Q1 , median, and Q3 form a set of descriptive statistics called the

Answer 84

five-number summary.

Question 85

box plot (4)

Answer 85

1. is a data visualization that uses a box and several lines to depict the distribution of data in a dataset. 2. A box spans 50% the middle of the data, with Q1 as the lower boundary of the box and Q3 as the upper boundary of the box. 3. The median is shown as a line inside the box. Two lines, known as whiskers, extend from the lower boundary of the box to the minimum and from the upper boundary of the box to the maximum. 4. The whiskers represent the lower and upper 25% of the data.

Question 86

Skew (2)

Answer 86

1. is the difference between the mean and the median 2. A positive skew means that the distribution is skewed to the right, while a negative skew means that the distribution is skewed to the left.

Question 87

Detecting outliers (3)

Answer 87

1. One way to detect outliers using a box plot is to determine how far each data element is from either Q1 or Q3. 2. A data value greater than Q3 + 1.5(IQR) or less than Q1 - 1.4(IQR) is considered an outlier. 3. Often, an outlier is not included in either whisker and is instead represented in the plot as a marker such as an open circle or a triangle.

Question 88

interquartile range (IQR) OF A DATASET

Answer 88

1. is the difference between Q3 and Q1 (Q3 - Q1), or the length of the box in a box plot.

Question 89

frequency distribution (2)

Answer 89

1. is a table that displays how often an outcome occurs for a sample 2. To construct a frequency distribution, the data set is divided into mutually exclusive classeS

Question 90

class

Answer 90

is either a value of a categorical variable or an interval of a continuous variable.

Question 91

frequency of a class

Answer 91

is the number of events or values that fall under each class.

Question 92

The most common graphical representation of a frequency distribution is a

Answer 92

histogram

Question 93

histogram

Answer 93

depicts data values by splitting a continuous variable into a number of class intervals, each known as a bin.

Question 94

A key goal of a histogram is to:

Answer 94

1. estimate the probability density function of the continuous variable on the X-axis. 2. In short, the goal is to fit a smooth curve over the most rectangles, while minimizing the white space under the curve.

Question 95

unimodal distribution

Answer 95

occurs when one mode exists in the histogram.

Question 96

Bimodal:

Answer 96

Contains two prevalent modes

Question 97

multimodal

Answer 97

Contains multiple prevalent modes

Question 98

Skewed left:

Answer 98

Contains a mode on the right with a tail of low-frequency bins on the left

Question 99

Skewed right:

Answer 99

Contains a mode on the left with a tail of low-frequency bins on the right

Question 100

line chart (3)

Answer 100

1. depicts data trends by using straight lines to connect successive data points in a scatter plot. 2. The straight lines show the general direction that data changes over time. 3. Because trends involve time, line charts commonly use a time metric for the horizontal axis.

Question 101

main benefit of a line graph is to (2)

Answer 101

1. quickly convey whether values are increasing, decreasing, or remaining constant between data points. 2. Steeper lines indicate more rapid increases or decreases, while flatter lines indicate little change between data points

Question 102

linear trend line

Answer 102

is a straight line that depicts the general direction data changes from the first to last data point, often added to summarize the entire chart

Question 103

A line chart should not be used for (2)

Answer 103

1. nominal categorical data. 2. Lines suggest some relation from one item to the next, but nominal variables have no ordering so can have no such relation.

Question 103

bar chart (2)

Answer 103

1. depicts data values for a categorical variable, using rectangular bars having lengths proportional to category values. 2. The chart is drawn using two axes: a category axis that displays the category names and a value axis that displays the counts

Question 104

relative-frequency bar chart

Answer 104

shows each category's portion of the total data, typically as a percentage.