Praxis (5511) - Fundamental Subjects: Content Knowledge > 6 - Data Analysis and Probability Skills > Flashcards

6 - Data Analysis and Probability Skills Flashcards

This deck focuses on interpreting data from charts, graphs, tables, and spreadsheets, identifying trends and patterns, and making inferences. It also covers calculating and comparing mean, median, mode, and range, as well as solving various problems using probability concepts. (74 cards)

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1
Q

Identify:

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

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

Define:

graph

A

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

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3
Q

Identify:

The three major types of graphs.

A
  • Bar graphs
  • Line graphs
  • Pie charts
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4
Q

Explain:

The purpose of a graph title.

A

To explain what the graph is about.

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5
Q

Explain:

What does the x-axis represent in a graph?

A

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

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6
Q

Explain:

What does the y-axis represent in a graph?

A

It is vertical and typically made up of numbers.

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7
Q

Explain:

The function of a graph legend.

A

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

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8
Q

When should you use a bar graph?

A

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

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9
Q

Explain:

When is line graph most appropriate to use?

A

To show change over time with connected data points.

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10
Q

Explain:

When is pie chart most appropiate to use?

A

When representing parts of a whole, often in percentages.

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11
Q

Identify:

Where does the x-axis runs along the graph?

A

bottom

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12
Q

Identify:

Where does the y-axis run along the graph?

A

left

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13
Q

Describe:

line graph

A

A graph with a line connecting data points.

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

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14
Q

Explain:

How to read a line graph.

A

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.

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15
Q

Explain:

What it means if the line on a graph increases?

A

It suggests that the measured variable is increasing over time.

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

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16
Q

Explain:

What is indicated if the line on a graph decreases?

A

The variable being measured is declining.

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

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17
Q

Explain:

The primary use of a bar graph.

A

To compare different sets of data within a group.

Bar graphs can also show changes over time.

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18
Q

Explain:

The primary use of a pie chart.

A

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

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19
Q

Identify:

What do bars in a bar graph represent?

A

Data measurements.

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

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20
Q

Describe:

How is data presented in a bar graph?

A

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

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21
Q

Identify:

What is an important aspect of reading a bar graph?

A

Intervals on the scale.

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

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22
Q

Identify:

What does a pie chart represent?

A

The entire amount or 100%.

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

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23
Q

Identify:

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

A

They should add up to 100%.

This allows for easy comparison of the parts.

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24
Q

Explain:

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

A

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).

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25
# Identify What type of **graph** uses rectangular bars to represent data?
bar graph ## Footnote Bar graphs can be displayed horizontally or vertically.
26
# Define: measures of central tendency
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.
27
# Define: descriptive statistics
A type of statistics used to describe and summarize values in a data set.
28
# Define: mean
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.
29
# Explain: 3 steps to find the **mean**.
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.
30
# Define: median
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.
31
# Explain: How can you find the **median** when the data set has an **odd quantity of numbers**?
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.
32
# Explain: How can you find the **median** when the data set has an **even quantity of numbers**?
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.
33
# Define: mode
The number or value that occurs the most in a data set. ## Footnote Useful for categorical data, which can be organized into groups.
34
# Explain: Steps to find the **mode**.
1. Organize data by groups or magnitude. 2. Identify the value that occurs most frequently within the set.
35
# Define: range
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.
36
# Identify: Formula for finding the **range**.
Maximum value minus minimum value. ## Footnote Range provides the spread of a data set.
37
In what type of distribution are the **mean**, **median** and **mode** all at the **center**?
Symmetrical distribution. ## Footnote Often visualized as a bell-curve.
38
# Describe: skewed distribution
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.
39
# Define: descriptive statistics
A type of statistics used to describe and summarize values in a data set. ## Footnote It does not provide information about individual values.
40
# Define: categorical data
Data that can be organized into groups but **does not have mathematical meaning**. ## Footnote Examples include zip codes and phone numbers.
41
# Define: outlier
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.
42
# Explain: How does **skewness** affect the **mean**?
The more a distribution is skewed, the less accurate the mean. ## Footnote The median may provide a better representation in skewed distributions.
43
# Define: probability
**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.
44
# Identify: The **range** of probability values.
0 to 1 ## Footnote Zero indicates an impossible event, while one indicates a certain event.
45
# Identify: The **formula** for calculating probability.
Probability = Favorable Outcomes / Total Outcomes ## Footnote This formula helps determine the likelihood of specific events.
46
# Define: simple probability
The probability of one event happening. ## Footnote It uses the formula Probability = Favorable Outcomes / Total Outcomes.
47
# Identify: **simple probability** example
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.
48
# Define: sequential probability
The probability of two or more events occurring. ## Footnote It can involve dependent or independent events.
49
# Define: dependent events
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.
50
# Define: independent events
Events where the **outcome of one does not affect the outcome of another**. ## Footnote Example: Flipping a coin and rolling dice.
51
# Explain: How do you calculate **sequential probability**?
* Find the probability of the events like in a simple probability. * Multiply the probabilities together. ## Footnote Keep the probabilities in fraction form when multiplying.
52
# Identify: 3 ways to express probability
1. Fraction 1. Ratio 1. Percentage ## Footnote Each format is useful in different contexts.
53
# Explain: What is the probability of picking an apple from a bowl containing 4 apples and 10 total fruits, expressed as a fraction?
4/10 ## Footnote This can also be expressed as a ratio (4:10) or percentage (40%).
54
# Explain: What does a **probability line** indicate?
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.
55
# Explain: Why is **probability** relevant in daily life?
It helps predict outcomes in situations like weather forecasts or sports events. ## Footnote Understanding probability aids decision-making based on likelihood.
56
# Define: marginal probability
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.
57
# Define: The **complement** of an event.
The event not occurring, commonly notated as A′ or Ac.
58
# Define: joint probability
The likelihood of two events occurring at the same time, notated as P(A⋂B).
59
# Define: conditional probability
The likelihood of an event occurring given that a different event has already occurred, notated as P(A|B).
60
# Identify: The formula for **basic (marginal) probability**.
P(A) = number of ways A can occur / total number of possible outcomes.
61
# Identify: The formula for **complement probability**.
P(A′) = 1 - P(A)
62
# Identify: The joint probability formula for independent events.
P(A⋂B) = P(A) ⋅ P(B)
63
# Explain: What does it mean for events to be **mutually exclusive**?
They can never happen simultaneously, notated as P(A⋂B) = 0.
64
# Explain: What is the **addition law of probability**?
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).
65
# Identify: The **formula** to calculate the **probability of occurrence for three or more disjoint events**.
P(A⋃B⋃C) = P(A) + P(B) + P(C)
66
# Explain: What is **conditional probability**?
If the probability of an event occurring depends on another or a prior event, it is said to be conditional.
67
# Identify: Conditional probability formula.
P(A|B) = P(A⋂B) / P(B)
68
# Identify: The formula for calculating the **Law of Total Probability**.
P(A) = P(A⋂B) + P(A⋂C)
69
# Explain: The **Bayes' Theorem**
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.
70
# Explain: Law of Total Probability
It states that the probability of an event is equal to the sum of the probabilities of its components.
71
# Identify: 3 laws of probability
1. Multiplication rule 1. Addition rule 1. Complement rule
72
# Describe: The **multiplication law** of probability.
It is used when calculating the probability of A and B. The two probabilities are multiplied together.
73
# Describe: The **addition rule** of probability.
* 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.
74
# Describe: The **compliment rule** of probability.
It is used when calculating the probability of anything besides A. The probability of A not occurring is 1-P(A).
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