Podcast
Questions and Answers
What symbol is used to denote the standard deviation of a sample?
What symbol is used to denote the standard deviation of a sample?
- V
- s (correct)
- μ
- σ
The variance is the square root of the standard deviation.
The variance is the square root of the standard deviation.
False (B)
How is the variance calculated from the standard deviation?
How is the variance calculated from the standard deviation?
It is calculated by squaring the standard deviation.
The standard deviation is denoted by the Greek letter __________ for a population.
The standard deviation is denoted by the Greek letter __________ for a population.
Match the following terms with their definitions:
Match the following terms with their definitions:
What is the branch of statistics that focuses on collecting and organizing data?
What is the branch of statistics that focuses on collecting and organizing data?
The mode is the only measure of central tendency that represents the average of a set of numbers.
The mode is the only measure of central tendency that represents the average of a set of numbers.
What symbol is traditionally used to indicate summation in statistics?
What symbol is traditionally used to indicate summation in statistics?
The mean of a population is denoted by the Greek letter _____.
The mean of a population is denoted by the Greek letter _____.
From the provided data: 92, 84, 65, 76, 88, and 90, what is the mean test score?
From the provided data: 92, 84, 65, 76, 88, and 90, what is the mean test score?
The median is always the same as the mean in a dataset.
The median is always the same as the mean in a dataset.
The _____ is the middle number in a dataset arranged in order.
The _____ is the middle number in a dataset arranged in order.
What is the standard deviation of Data B?
What is the standard deviation of Data B?
In a normal distribution, the mean, median, and mode are all equal.
In a normal distribution, the mean, median, and mode are all equal.
What is the variance of a standard deviation of 5?
What is the variance of a standard deviation of 5?
The total area under the normal curve is equal to _____?
The total area under the normal curve is equal to _____?
What is Dillon's GPA for the fall semester?
What is Dillon's GPA for the fall semester?
Which of the following statements about a normal distribution is NOT true?
Which of the following statements about a normal distribution is NOT true?
Match the data set to its corresponding standard deviation:
Match the data set to its corresponding standard deviation:
The range of a data set is calculated by finding the sum of all values.
The range of a data set is calculated by finding the sum of all values.
What is the significance of standard deviation in statistics?
What is the significance of standard deviation in statistics?
How many total weights were used to calculate Dillon's GPA?
How many total weights were used to calculate Dillon's GPA?
In a normal distribution, the graph is _____-shaped and symmetrical about the mean.
In a normal distribution, the graph is _____-shaped and symmetrical about the mean.
The standard deviation is a measure of ____ that is less sensitive to extreme values.
The standard deviation is a measure of ____ that is less sensitive to extreme values.
Which of these values is used to calculate the weighted mean?
Which of these values is used to calculate the weighted mean?
The sum of all deviations from the mean is always positive.
The sum of all deviations from the mean is always positive.
To find the range (R), the formula is R = ____ - ____.
To find the range (R), the formula is R = ____ - ____.
What is the cumulative area for a z-score of 0?
What is the cumulative area for a z-score of 0?
The cumulative area for z-scores close to z = 3.49 is close to 0.
The cumulative area for z-scores close to z = 3.49 is close to 0.
What is the formula for calculating a z-score?
What is the formula for calculating a z-score?
The standard normal distribution has a mean of ______ and a standard deviation of ______.
The standard normal distribution has a mean of ______ and a standard deviation of ______.
Which of the following best describes the cumulative area as z-scores increase?
Which of the following best describes the cumulative area as z-scores increase?
What z-score corresponds to an area of approximately 0.8749?
What z-score corresponds to an area of approximately 0.8749?
Match the cumulative area with the corresponding z-score:
Match the cumulative area with the corresponding z-score:
The z-score formula is z = _______.
The z-score formula is z = _______.
What is the median of the list 4, 8, 1, 14, 9, 21, 12?
What is the median of the list 4, 8, 1, 14, 9, 21, 12?
The mode of the list 18, 15, 21, 16, 15, 14, 15, 21 is 21.
The mode of the list 18, 15, 21, 16, 15, 14, 15, 21 is 21.
What do you call a list of numbers arranged from smallest to largest?
What do you call a list of numbers arranged from smallest to largest?
In a list with an even number of entries, the median is found by calculating the mean of the two ____ numbers.
In a list with an even number of entries, the median is found by calculating the mean of the two ____ numbers.
Match the type of average with its definition:
Match the type of average with its definition:
What is the weighted mean of scores 65, 70, 75 with a final examination score of 90 where the final exam counts as 2 tests?
What is the weighted mean of scores 65, 70, 75 with a final examination score of 90 where the final exam counts as 2 tests?
There can be more than one mode in a dataset.
There can be more than one mode in a dataset.
What is the mode of the list 2, 5, 8, 9, 11, 4, 7, 23?
What is the mode of the list 2, 5, 8, 9, 11, 4, 7, 23?
What is the median of the following list: 46, 23, 92, 89, 77, 108?
What is the median of the following list: 46, 23, 92, 89, 77, 108?
The mode of the list 2, 5, 8, 9, 11, 4, 7, 23 is 5.
The mode of the list 2, 5, 8, 9, 11, 4, 7, 23 is 5.
What is a ranked list?
What is a ranked list?
When finding the median of a list with an _____ number of entries, rank the numbers and find the middle number.
When finding the median of a list with an _____ number of entries, rank the numbers and find the middle number.
Match the following statistical measures with their definitions:
Match the following statistical measures with their definitions:
What is the mode of the list: 18, 15, 21, 16, 15, 14, 15, 21?
What is the mode of the list: 18, 15, 21, 16, 15, 14, 15, 21?
The weighted mean assigns equal importance to all data points.
The weighted mean assigns equal importance to all data points.
If a professor counts the final examination score as two test scores, what kind of average is being calculated?
If a professor counts the final examination score as two test scores, what kind of average is being calculated?
The range is calculated by subtracting the minimum value from the maximum value.
The range is calculated by subtracting the minimum value from the maximum value.
What is the formula used to compute the range of a data set?
What is the formula used to compute the range of a data set?
The weighted mean formula accounts for the _____ of each grade.
The weighted mean formula accounts for the _____ of each grade.
Match the statistical measure with its description:
Match the statistical measure with its description:
Which statistical measure is less sensitive to extreme values?
Which statistical measure is less sensitive to extreme values?
What measure of central tendency is represented by the symbol 'x̄'?
What measure of central tendency is represented by the symbol 'x̄'?
Inferential statistics focuses on collecting and organizing data.
Inferential statistics focuses on collecting and organizing data.
What is the term used for a small portion of a larger group in statistics?
What is the term used for a small portion of a larger group in statistics?
The median is the ______ number in a dataset arranged in order.
The median is the ______ number in a dataset arranged in order.
Match the following measures of central tendency with their definitions:
Match the following measures of central tendency with their definitions:
Which of the following describes a dataset that has no mode?
Which of the following describes a dataset that has no mode?
The arithmetic mean is the most basic measure of central tendency.
The arithmetic mean is the most basic measure of central tendency.
What is the Greek letter used to denote the mean of a population?
What is the Greek letter used to denote the mean of a population?
The cumulative area is close to 1 for z-scores close to z = -3.49.
The cumulative area is close to 1 for z-scores close to z = -3.49.
What does the z-score formula help to determine?
What does the z-score formula help to determine?
To transform a value into a z-score, the __________ must be subtracted from the value.
To transform a value into a z-score, the __________ must be subtracted from the value.
Match the following z-scores with their corresponding cumulative area:
Match the following z-scores with their corresponding cumulative area:
What area corresponds to a z-score of 1.15?
What area corresponds to a z-score of 1.15?
As the z-scores increase, the cumulative area under the standard normal curve decreases.
As the z-scores increase, the cumulative area under the standard normal curve decreases.
Which z-score corresponds to a cumulative area close to 1?
Which z-score corresponds to a cumulative area close to 1?
What is the standard deviation of Data A, which has a mean of 15.5?
What is the standard deviation of Data A, which has a mean of 15.5?
The mean, median, and mode of a normal distribution are all equal.
The mean, median, and mode of a normal distribution are all equal.
What is the area to the left of z = -0.24?
What is the area to the left of z = -0.24?
The area to the right of z = 1.23 is equal to 0.1093.
The area to the right of z = 1.23 is equal to 0.1093.
What is the variance when the standard deviation is 8?
What is the variance when the standard deviation is 8?
In a normal distribution, the total area under the curve is equal to _____.
In a normal distribution, the total area under the curve is equal to _____.
Match the following standard deviations with their corresponding variances:
Match the following standard deviations with their corresponding variances:
To find the area between two z-scores, subtract the area of the smaller z-score from the area of the larger one. The area left of z = 1.23 is 0.8907 and the area left of z = -0.75 is __________.
To find the area between two z-scores, subtract the area of the smaller z-score from the area of the larger one. The area left of z = 1.23 is 0.8907 and the area left of z = -0.75 is __________.
Which of the following statements about the heights of the players in Team A is true?
Which of the following statements about the heights of the players in Team A is true?
How would you find the area to the right of z = 1.06?
How would you find the area to the right of z = 1.06?
Match the z-scores with their corresponding areas.
Match the z-scores with their corresponding areas.
A normal distribution can have a mean of any value, but its standard deviation must be greater than zero.
A normal distribution can have a mean of any value, but its standard deviation must be greater than zero.
The total area under the standard normal curve is greater than 1.
The total area under the standard normal curve is greater than 1.
The standard deviation is a measure of _____ that indicates the amount of variability in a dataset.
The standard deviation is a measure of _____ that indicates the amount of variability in a dataset.
What is the process to find the area between two z-scores?
What is the process to find the area between two z-scores?
What is the standard deviation of the sample with the following values: 2, 4, 7, 12, 15?
What is the standard deviation of the sample with the following values: 2, 4, 7, 12, 15?
What is the formula used to calculate the sample standard deviation?
What is the formula used to calculate the sample standard deviation?
The standard deviation of a population is denoted by the Greek letter __________.
The standard deviation of a population is denoted by the Greek letter __________.
What is the term for the average that is calculated by summing a set of values and dividing by the number of values?
What is the term for the average that is calculated by summing a set of values and dividing by the number of values?
Inferential statistics focuses on collecting and organizing data to summarize and present it.
Inferential statistics focuses on collecting and organizing data to summarize and present it.
What notation is traditionally used to denote the sum of a set of numbers in statistics?
What notation is traditionally used to denote the sum of a set of numbers in statistics?
The __________ is the value that separates the higher half from the lower half of a dataset when arranged in order.
The __________ is the value that separates the higher half from the lower half of a dataset when arranged in order.
Match each term with its definition:
Match each term with its definition:
Which of the following is NOT a measure of central tendency?
Which of the following is NOT a measure of central tendency?
The mean of a sample is denoted by the symbol μ (mu).
The mean of a sample is denoted by the symbol μ (mu).
If a set of numbers is {5, 10, 15, 20, 25}, what is the median?
If a set of numbers is {5, 10, 15, 20, 25}, what is the median?
What shape is the graph of a normal distribution?
What shape is the graph of a normal distribution?
Match the following data sets with their standard deviation:
Match the following data sets with their standard deviation:
Which of the following describes the characteristic of the standard deviation?
Which of the following describes the characteristic of the standard deviation?
Standard deviation can be zero if all data points are the same.
Standard deviation can be zero if all data points are the same.
What does the mean of a normal distribution indicate?
What does the mean of a normal distribution indicate?
The points at which the normal curve changes from curving upward to curving downward are known as the mean points.
The points at which the normal curve changes from curving upward to curving downward are known as the mean points.
For a standard normal distribution, what is the mean value?
For a standard normal distribution, what is the mean value?
In a normal distribution, the standard deviation describes the __________ of the data.
In a normal distribution, the standard deviation describes the __________ of the data.
Match the following components of a normal distribution with their descriptions:
Match the following components of a normal distribution with their descriptions:
Which of the following normal distributions has a greater standard deviation?
Which of the following normal distributions has a greater standard deviation?
The normal curve approaches the x-axis, touching it, as it extends away from the mean.
The normal curve approaches the x-axis, touching it, as it extends away from the mean.
What would be an estimated value of the standard deviation if the mean test score is approximately 675 and the inflection points are one standard deviation away from the mean?
What would be an estimated value of the standard deviation if the mean test score is approximately 675 and the inflection points are one standard deviation away from the mean?
What is the cumulative area corresponding to a z-score of 0?
What is the cumulative area corresponding to a z-score of 0?
The cumulative area under the standard normal curve approaches _____ for z-scores of 3.49.
The cumulative area under the standard normal curve approaches _____ for z-scores of 3.49.
If a z-score is 1.15, what is the cumulative area to the left of this score?
If a z-score is 1.15, what is the cumulative area to the left of this score?
Match the z-score with its cumulative area:
Match the z-score with its cumulative area:
The standard normal distribution has a mean of 1 and a standard deviation of 0.
The standard normal distribution has a mean of 1 and a standard deviation of 0.
What happens to the cumulative area as z-scores increase?
What happens to the cumulative area as z-scores increase?
The area to the right of z = 1.23 is calculated by subtracting the area to the left from 0.
The area to the right of z = 1.23 is calculated by subtracting the area to the left from 0.
To find the area between two z-scores, you subtract the area of the smaller z-score from the area of the ______ z-score.
To find the area between two z-scores, you subtract the area of the smaller z-score from the area of the ______ z-score.
What is the area to the right of z = 1.23?
What is the area to the right of z = 1.23?
Match the following z-scores with their respective areas:
Match the following z-scores with their respective areas:
The cumulative area under the standard normal curve always equals 1.
The cumulative area under the standard normal curve always equals 1.
What is the area between z = -0.99 and z = 1.23?
What is the area between z = -0.99 and z = 1.23?
What term is used to describe the average of a sample in statistics?
What term is used to describe the average of a sample in statistics?
The median is always the largest number in a dataset.
The median is always the largest number in a dataset.
Define the term 'population' in statistics.
Define the term 'population' in statistics.
The mean of a dataset is also referred to as the __________ mean.
The mean of a dataset is also referred to as the __________ mean.
Which of the following represents the process of narrowing down a large population to a subset for analysis?
Which of the following represents the process of narrowing down a large population to a subset for analysis?
The summation symbol is represented by the letter 'S'.
The summation symbol is represented by the letter 'S'.
What is the formula to calculate the arithmetic mean of a dataset?
What is the formula to calculate the arithmetic mean of a dataset?
What is the weighted mean formula used to find Dillon’s GPA based on the weights of his grades?
What is the weighted mean formula used to find Dillon’s GPA based on the weights of his grades?
The range is a measure of dispersion that averages all values in a dataset.
The range is a measure of dispersion that averages all values in a dataset.
Calculate the range of the pulse rates: 54, 58, 58, 60, 62, 65, 66, 71, 74, 75, 77, 78, 80, 82, 85.
Calculate the range of the pulse rates: 54, 58, 58, 60, 62, 65, 66, 71, 74, 75, 77, 78, 80, 82, 85.
The standard deviation is less sensitive to ______ values than the range.
The standard deviation is less sensitive to ______ values than the range.
From the provided weights to find Dillon’s GPA, which weight corresponded to the grade D?
From the provided weights to find Dillon’s GPA, which weight corresponded to the grade D?
The sum of deviations from the mean in any dataset is always equal to zero.
The sum of deviations from the mean in any dataset is always equal to zero.
What is the standard deviation used for in statistics?
What is the standard deviation used for in statistics?
What is the correct formula to calculate the variance from a given standard deviation?
What is the correct formula to calculate the variance from a given standard deviation?
The standard deviation of a sample is denoted by the Greek letter sigma.
The standard deviation of a sample is denoted by the Greek letter sigma.
If the sample has the numbers 2, 4, 7, 12, and 15, what is the mean of this sample?
If the sample has the numbers 2, 4, 7, 12, and 15, what is the mean of this sample?
The standard deviation is calculated using the formula: s = √[Σ(x - mean)² / (n - 1)], where 'n' is the sample size. In this case, 'n' is equal to _____ for the sample provided.
The standard deviation is calculated using the formula: s = √[Σ(x - mean)² / (n - 1)], where 'n' is the sample size. In this case, 'n' is equal to _____ for the sample provided.
Match the following symbols to their corresponding descriptions:
Match the following symbols to their corresponding descriptions:
The cumulative area increases as z-scores decrease.
The cumulative area increases as z-scores decrease.
What is the cumulative area close to for z-scores near z = 3.49?
What is the cumulative area close to for z-scores near z = 3.49?
The formula to find the z-score is z = ______.
The formula to find the z-score is z = ______.
Which z-score has a cumulative area closest to 0?
Which z-score has a cumulative area closest to 0?
The cumulative area to the left of z = 1.15 is greater than 0.9000.
The cumulative area to the left of z = 1.15 is greater than 0.9000.
How does the cumulative area behave as z-scores increase?
How does the cumulative area behave as z-scores increase?
The area to the right of z = 1.23 can be found by subtracting the area to the left from 1.
The area to the right of z = 1.23 can be found by subtracting the area to the left from 1.
What is the area under the standard normal curve to the left of z = –0.99?
What is the area under the standard normal curve to the left of z = –0.99?
To find the area between two z-scores, you need to subtract the area of the _____ from the area of the higher z-score.
To find the area between two z-scores, you need to subtract the area of the _____ from the area of the higher z-score.
If the area to the left of z = –0.75 is 0.2266, what is the area between z = –0.75 and z = 1.23?
If the area to the left of z = –0.75 is 0.2266, what is the area between z = –0.75 and z = 1.23?
Match the z-score with its corresponding area under the standard normal curve.
Match the z-score with its corresponding area under the standard normal curve.
The total area under the standard normal curve equals 1.
The total area under the standard normal curve equals 1.
The area to the right of z = 1.06 can be found by subtracting the area to the left from _____ .
The area to the right of z = 1.06 can be found by subtracting the area to the left from _____ .
What is the standard deviation of Team A's heights in inches?
What is the standard deviation of Team A's heights in inches?
The total area under a normal distribution curve is equal to 0.
The total area under a normal distribution curve is equal to 0.
What shape does the normal distribution curve typically have?
What shape does the normal distribution curve typically have?
In a normal distribution, the mean, median, and mode are all equal at __________.
In a normal distribution, the mean, median, and mode are all equal at __________.
Match the standard deviation with its corresponding variance:
Match the standard deviation with its corresponding variance:
Which data set has the highest standard deviation?
Which data set has the highest standard deviation?
The mean of Team B's heights is greater than the mean of Team A's heights.
The mean of Team B's heights is greater than the mean of Team A's heights.
The variance is defined as the __________ of the standard deviation.
The variance is defined as the __________ of the standard deviation.
Flashcards
Arithmetic Mean
Arithmetic Mean
The sum of a set of numbers divided by the count of those numbers.
Summation Notation
Summation Notation
Using the Greek letter sigma (Σ) to represent the sum of a set of numbers.
Population
Population
The entire group being studied.
Sample
Sample
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Mean of a Sample
Mean of a Sample
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Mean of a Population
Mean of a Population
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Descriptive Statistics
Descriptive Statistics
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Inferential Statistics
Inferential Statistics
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Ranked List
Ranked List
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Median (Odd)
Median (Odd)
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Median (Even)
Median (Even)
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Mode
Mode
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Mode (No Mode)
Mode (No Mode)
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Weighted Mean
Weighted Mean
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Weighting
Weighting
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Example of Weighted Mean
Example of Weighted Mean
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Standard Deviation
Standard Deviation
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Sample Standard Deviation
Sample Standard Deviation
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Population Standard Deviation
Population Standard Deviation
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Variance
Variance
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Calculating Standard Deviation
Calculating Standard Deviation
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What is the range?
What is the range?
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Sum of Deviations
Sum of Deviations
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Why Use Squares?
Why Use Squares?
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GPA Calculation
GPA Calculation
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Dispersion vs. Central Tendency
Dispersion vs. Central Tendency
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Sensitivity to Outliers
Sensitivity to Outliers
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Standard Deviation (s)
Standard Deviation (s)
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Example: Standard Deviation and Variance
Example: Standard Deviation and Variance
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Comparing Standard Deviation
Comparing Standard Deviation
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Normal Distribution
Normal Distribution
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Normal Curve
Normal Curve
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Area Under Normal Curve
Area Under Normal Curve
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Standard Normal Curve
Standard Normal Curve
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Z-Score
Z-Score
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Standard Normal Distribution
Standard Normal Distribution
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Cumulative Area
Cumulative Area
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Standard Normal Table
Standard Normal Table
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Finding Area for a Z-Score
Finding Area for a Z-Score
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Area Close to 0
Area Close to 0
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Area Close to 1
Area Close to 1
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Area at Z=0
Area at Z=0
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What is the arithmetic mean?
What is the arithmetic mean?
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What is descriptive statistics?
What is descriptive statistics?
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What is inferential statistics?
What is inferential statistics?
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What is a sample?
What is a sample?
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What is a population?
What is a population?
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What is the median?
What is the median?
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What is summation notation?
What is summation notation?
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What is the mode?
What is the mode?
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Range
Range
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Why Squares?
Why Squares?
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How to find the area for a given z-score?
How to find the area for a given z-score?
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Area Under the Curve
Area Under the Curve
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Area to the Left of Z
Area to the Left of Z
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Area to the Right of Z
Area to the Right of Z
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Area Between Two Z-Scores
Area Between Two Z-Scores
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Inflection Points
Inflection Points
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Mean and Standard Deviation
Mean and Standard Deviation
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Greater Mean
Greater Mean
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Greater Standard Deviation
Greater Standard Deviation
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Interpreting a Graph
Interpreting a Graph
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Approaching the x-axis
Approaching the x-axis
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What is the standard normal table used for?
What is the standard normal table used for?
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What is the cumulative area in relation to the standard normal distribution?
What is the cumulative area in relation to the standard normal distribution?
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What is the area under the curve?
What is the area under the curve?
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How can we find the area for a given z-score?
How can we find the area for a given z-score?
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What are the key properties of the standard normal distribution?
What are the key properties of the standard normal distribution?
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What is a normal distribution?
What is a normal distribution?
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What are the types of statistics?
What are the types of statistics?
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What is the range sensitive to?
What is the range sensitive to?
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Why are deviations squared?
Why are deviations squared?
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How to calculate GPA?
How to calculate GPA?
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What is dispersion?
What is dispersion?
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Central Tendency vs. Dispersion
Central Tendency vs. Dispersion
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What is the area to the left of z?
What is the area to the left of z?
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What is the area to the right of z?
What is the area to the right of z?
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What is the area between two z-scores?
What is the area between two z-scores?
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Study Notes
Chapter 4.1: Statistics
- Statistics involves collecting, organizing, summarizing, presenting, and interpreting data.
- Descriptive statistics involves collecting, organizing, summarizing, and presenting data.
- Inferential statistics interprets data and draws conclusions.
Measures of Central Tendency
- Averages are measures of central tendency for numerical data.
- Three types of averages are the arithmetic mean, median, and mode.
The Arithmetic Mean
- The arithmetic mean is the sum of the numbers divided by the number of values.
- Summation notation (Σx) denotes the sum of all numbers in a set.
- The mean of n numbers is calculated as Σx / n.
- Sample mean (x̄) is used for samples.
- Population mean (µ) is used for populations.
Example 1: Finding a Mean
- Six students' test scores (92, 84, 65, 76, 88, 90)
- Calculating the mean: (92 + 84 + 65 + 76 + 88 + 90) / 6 = 82.5
The Median
- The median is the middle number in a ranked list (ordered from smallest to largest or largest to smallest).
- If the number of values is odd, the median is the middle value.
- If the number of values is even, the median is the mean of the two middle values.
Example 2: Finding a Median
- Data sets are ranked.
- Median determined based on the number of elements.
- Odd number of elements: the middle number is the median.
- Even number of elements: the mean of two middle numbers is the median.
The Mode
- Mode is the number that appears most frequently in a list.
- A data set can have more than one mode or no mode.
Example 3: Finding a Mode
- Determining the most frequent number in a set.
The Weighted Mean
- Used when some data values are more important than others.
- Each score is assigned a weight.
- Calculation: Σ(x · w) / Σw, where x is each score, w is the corresponding weight.
Example 4: Finding a Weighted Mean
- Calculating GPA using course grades and units.
Chapter 4.2: Measures of Dispersion
- Range and standard deviation are statistical measures of dispersion.
The Range
- Range is the difference between the greatest and least values in a dataset.
- Calculation: Range = Max - Min
Example 1: Finding a Range
- Calculating range from a dataset of pulse rates.
The Standard Deviation
- Measures the amount by which each data value deviates from the mean.
- Deviations are calculated by subtracting the mean from each data value.
- Deviations can be positive or negative, and sum to zero.
- Standard deviation uses the sum of the squared deviations to determine the dispersion magnitude.
- Population standard deviation (σ) is calculated using Σ(x − μ)² / n.
- Sample standard deviation (s) is calculated using Σ(x − x̄)² / (n − 1).
Example 2: Finding a Standard Deviation
- Calculating standard deviation from a sample data given.
- Using this data calculate the variance and define the notations for population standard deviation and variance.
The Variance
- Variance is the square of the standard deviation.
- Variance is used as a measure of dispersion.
Example 5: Finding the Variance
- Calculating the variance using the standard deviation from example 2.
Normal Distribution and Areas Under the Normal Curve
- Normal distribution is a continuous probability distribution.
- Bell-shaped curve, symmetric about the mean.
- Mean, median, and mode are equal.
- The total area under the curve is 1.
- The normal curve approaches the x-axis but never touches it.
- Mean μ and Standard Deviation σ
- Inflection points are the change of concave nature from the graph curves.
- Find z score using: z= (value − mean) / standard deviation
Calculating Areas Under the Curve
- Tables are used to find the area under a part of the curve.
- Find z-score, then use the table to find the corresponding area.
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