6 - Data Analysis and Probability Skills

Question 1

Identify:

What are 3 real-world examples of the application of statistics and probability?

Answer 1

1. College acceptance rates.
2. Baseball analysis.
3. Probability of winning the lottery.

Question 2

Define:

graph

Answer 2

Visual of data presented on axes that sort relationships between variables.

Question 3

Identify:

The three major types of graphs.

Answer 3

• Bar graphs
• Line graphs
• Pie charts

Question 4

Explain:

The purpose of a graph title.

Answer 4

To explain what the graph is about.

Question 5

Explain:

What does the x-axis represent in a graph?

Answer 5

It is horizontal and can be made up of categories or numbers.

Question 6

Explain:

What does the y-axis represent in a graph?

Answer 6

It is vertical and typically made up of numbers.

Question 7

Explain:

The function of a graph legend.

Answer 7

To help interpret results, especially when there are multiple lines or bars.

Question 8

When should you use a bar graph?

Answer 8

When the numbers being looked at are independent of each other.

Question 9

Explain:

When is line graph most appropriate to use?

Answer 9

To show change over time with connected data points.

Question 10

Explain:

When is pie chart most appropiate to use?

Answer 10

When representing parts of a whole, often in percentages.

Question 11

Identify:

Where does the x-axis runs along the graph?

Answer 11

bottom

Question 12

Identify:

Where does the y-axis run along the graph?

Answer 12

left

Question 13

Describe:

line graph

Answer 13

A graph with a line connecting data points.

Line graphs can show trends over time and provide visual insights into data.

Question 14

Explain:

How to read a line graph.

Answer 14

Look at the x-axis, draw an imaginary line up to the data point, and then draw another line to the y-axis for the value.

This method allows you to accurately determine the value associated with a specific data point.

Question 15

Explain:

What it means if the line on a graph increases?

Answer 15

It suggests that the measured variable is increasing over time.

This can indicate growth, improvement or an upward trend in performance.

Question 16

Explain:

What is indicated if the line on a graph decreases?

Answer 16

The variable being measured is declining.

This indicates a decrease or reduction in the performance or value over time.

Question 17

Explain:

The primary use of a bar graph.

Answer 17

To compare different sets of data within a group.

Bar graphs can also show changes over time.

Question 18

Explain:

The primary use of a pie chart.

Answer 18

Show how different sets of data compare to each other and to the whole.

Question 19

Identify:

What do bars in a bar graph represent?

Answer 19

Data measurements.

The length of each bar relates to the measurement in the data.

Question 20

Describe:

How is data presented in a bar graph?

Answer 20

One axis displays the categories, while the other axis shows the range of values.

Question 21

Identify:

What is an important aspect of reading a bar graph?

Answer 21

Intervals on the scale.

The scale often increases by larger units marked by tick marks.

Question 22

Identify:

What does a pie chart represent?

Answer 22

The entire amount or 100%.

It uses sectors to show the size or measurement of each part of the data.

Question 23

Identify:

What is the main requirement for all sectors in a pie chart?

Answer 23

They should add up to 100%.

This allows for easy comparison of the parts.

Question 24

Explain:

How can you calculate the number represented by a sector in a pie chart?

Answer 24

Multiply the percentage (as a decimal) by the total.

In this example, the amount of sales for Starbucks can be calculated by taking 14%, written as 0.14, and multiplying it by the total ($85 billion).

Question 25

# Identify What type of **graph** uses rectangular bars to represent data?

Answer 25

bar graph ## Footnote Bar graphs can be displayed horizontally or vertically.

Question 26

# Define: measures of central tendency

Answer 26

A set of numerical values that best represent or summarize the middle of a data set. ## Footnote Measures of central tendency include mean, median and mode.

Question 27

# Define: descriptive statistics

Answer 27

A type of statistics used to describe and summarize values in a data set.

Question 28

# Define: mean

Answer 28

The average of the individual values of a data set. ## Footnote Calculated by dividing the sum of all values by the total number of values.

Question 29

# Explain: 3 steps to find the **mean**.

Answer 29

1. Determine the total number of values within the dataset. 2. Determine the sum of the values in the data set. 3. Divide the sum of all the values by the total number of values in the dataset. ## Footnote This is synonymous with finding the average.

Question 30

# Define: median

Answer 30

The number in the middle of a data set with an equal number of values higher and lower than it. ## Footnote It can be found differently depending on whether the data set has an odd or even number of values.

Question 31

# Explain: How can you find the **median** when the data set has an **odd quantity of numbers**?

Answer 31

1. Organize the values in the set "by magnitude" (from least to greatest). 2. Find the value located directly in the middle of the set.

Question 32

# Explain: How can you find the **median** when the data set has an **even quantity of numbers**?

Answer 32

1. Organize values in the set by magnitude. 2. Find the two values that are located directly in the middle of the set. 3. Add the the two values together then divide the sum by two.

Question 33

# Define: mode

Answer 33

The number or value that occurs the most in a data set. ## Footnote Useful for categorical data, which can be organized into groups.

Question 34

# Explain: Steps to find the **mode**.

Answer 34

1. Organize data by groups or magnitude. 2. Identify the value that occurs most frequently within the set.

Question 35

# Define: range

Answer 35

The numerical difference between the maximum and minimum values of a data set. ## Footnote It indicates the spread of the data but can be misleading if there are extreme outliers.

Question 36

# Identify: Formula for finding the **range**.

Answer 36

Maximum value minus minimum value. ## Footnote Range provides the spread of a data set.

Question 37

In what type of distribution are the **mean**, **median** and **mode** all at the **center**?

Answer 37

Symmetrical distribution. ## Footnote Often visualized as a bell-curve.

Question 38

# Describe: skewed distribution

Answer 38

When the tail of a distribution on a graph is longer than the other side. ## Footnote Can be left-skewed or right-skewed depending on which side the tail is longer.

Question 39

# Define: descriptive statistics

Answer 39

A type of statistics used to describe and summarize values in a data set. ## Footnote It does not provide information about individual values.

Question 40

# Define: categorical data

Answer 40

Data that can be organized into groups but **does not have mathematical meaning**. ## Footnote Examples include zip codes and phone numbers.

Question 41

# Define: outlier

Answer 41

A value that is significantly higher or lower than the rest of the values in the data set. ## Footnote It can impact measures like the mean.

Question 42

# Explain: How does **skewness** affect the **mean**?

Answer 42

The more a distribution is skewed, the less accurate the mean. ## Footnote The median may provide a better representation in skewed distributions.

Question 43

# Define: probability

Answer 43

**Probability** is the likelihood that an event will happen, ranging from impossible (0) to certain (1). ## Footnote Examples include rolling a die or predicting weather outcomes.

Question 44

# Identify: The **range** of probability values.

Answer 44

0 to 1 ## Footnote Zero indicates an impossible event, while one indicates a certain event.

Question 45

# Identify: The **formula** for calculating probability.

Answer 45

Probability = Favorable Outcomes / Total Outcomes ## Footnote This formula helps determine the likelihood of specific events.

Question 46

# Define: simple probability

Answer 46

The probability of one event happening. ## Footnote It uses the formula Probability = Favorable Outcomes / Total Outcomes.

Question 47

# Identify: **simple probability** example

Answer 47

Probability of rolling an even number on a die. ## Footnote For example, if you roll a six-sided die, the chance of getting a two is 1 out of 6.

Question 48

# Define: sequential probability

Answer 48

The probability of two or more events occurring. ## Footnote It can involve dependent or independent events.

Question 49

# Define: dependent events

Answer 49

Events where the **outcome of one affects the outcome of another.** | Also called conditional events. ## Footnote Example: Taking a marble from a bag without replacement.

Question 50

# Define: independent events

Answer 50

Events where the **outcome of one does not affect the outcome of another**. ## Footnote Example: Flipping a coin and rolling dice.

Question 51

# Explain: How do you calculate **sequential probability**?

Answer 51

* Find the probability of the events like in a simple probability. * Multiply the probabilities together. ## Footnote Keep the probabilities in fraction form when multiplying.

Question 52

# Identify: 3 ways to express probability

Answer 52

1. Fraction 1. Ratio 1. Percentage ## Footnote Each format is useful in different contexts.

Question 53

# Explain: What is the probability of picking an apple from a bowl containing 4 apples and 10 total fruits, expressed as a fraction?

Answer 53

4/10 ## Footnote This can also be expressed as a ratio (4:10) or percentage (40%).

Question 54

# Explain: What does a **probability line** indicate?

Answer 54

It visually represents the likelihood of events from impossible (0) to certain (1). ## Footnote Markings on the line can show specific probabilities like 1/4 or 1/2.

Question 55

# Explain: Why is **probability** relevant in daily life?

Answer 55

It helps predict outcomes in situations like weather forecasts or sports events. ## Footnote Understanding probability aids decision-making based on likelihood.

Question 56

# Define: marginal probability

Answer 56

The likelihood of an event occurring without the influence of other events, notated as P(A). ## Footnote *P* stands for probability and *A* for an event occurring.

Question 57

# Define: The **complement** of an event.

Answer 57

The event not occurring, commonly notated as A′ or A^c.

Question 58

# Define: joint probability

Answer 58

The likelihood of two events occurring at the same time, notated as P(A⋂B).

Question 59

# Define: conditional probability

Answer 59

The likelihood of an event occurring given that a different event has already occurred, notated as P(A|B).

Question 60

# Identify: The formula for **basic (marginal) probability**.

Answer 60

P(A) = number of ways A can occur / total number of possible outcomes.

Question 61

# Identify: The formula for **complement probability**.

Answer 61

P(A′) = 1 - P(A)

Question 62

# Identify: The joint probability formula for independent events.

Answer 62

P(A⋂B) = P(A) ⋅ P(B)

Question 63

# Explain: What does it mean for events to be **mutually exclusive**?

Answer 63

They can never happen simultaneously, notated as P(A⋂B) = 0.

Question 64

# Explain: What is the **addition law of probability**?

Answer 64

It is useful when we want to calculate the probability of either one event *or* another happening. P(A⋃B) = P(A) + P(B) - P(A⋂B).

Question 65

# Identify: The **formula** to calculate the **probability of occurrence for three or more disjoint events**.

Answer 65

P(A⋃B⋃C) = P(A) + P(B) + P(C)

Question 66

# Explain: What is **conditional probability**?

Answer 66

If the probability of an event occurring depends on another or a prior event, it is said to be conditional.

Question 67

# Identify: Conditional probability formula.

Answer 67

P(A|B) = P(A⋂B) / P(B)

Question 68

# Identify: The formula for calculating the **Law of Total Probability**.

Answer 68

P(A) = P(A⋂B) + P(A⋂C)

Question 69

# Explain: The **Bayes' Theorem**

Answer 69

It is a formula used to find the probability of an event based on prior knowledge of related events. ## Footnote It converts one conditional probability to another.

Question 70

# Explain: Law of Total Probability

Answer 70

It states that the probability of an event is equal to the sum of the probabilities of its components.

Question 71

# Identify: 3 laws of probability

Answer 71

1. Multiplication rule 1. Addition rule 1. Complement rule

Question 72

# Describe: The **multiplication law** of probability.

Answer 72

It is used when calculating the probability of A and B. The two probabilities are multiplied together.

Question 73

# Describe: The **addition rule** of probability.

Answer 73

* It is used when calculating the probability of A or B. * The two probabilities are added together. * Then, the overlap is subtracted so it is not counted twice.

Question 74

# Describe: The **compliment rule** of probability.

Answer 74

It is used when calculating the probability of anything besides A. The probability of A not occurring is 1-P(A).