Statistics Quiz Flashcards

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Questions and Answers

What is the mean of the given test scores 92, 84, 65, 76, 88, 90?

85.0

80.5

90.0

82.5 (correct)

The median is always higher than the mean in a data set with a positive skew.

False

How would you interpret the 75th percentile in a data set?

It indicates that 75% of the data points are below that value.

The calculation of a Z-score indicates how many __________ a data point is from the mean.

standard deviations Signup and view all the answers

Match the following variables with their definitions:

Mean = Average value of a data set Median = Middle value when data is ordered Percentiles = Values that divide a data set into 100 equal parts Standard Deviation = Measure of data dispersion or spread Signup and view all the answers

What is used to measure the dispersion in a data set instead of the sum of the deviations?

Standard Deviation Signup and view all the answers

The sum of all deviations from the mean in any data set is greater than zero.

False Signup and view all the answers

What symbol is used to denote the standard deviation of a population?

σ Signup and view all the answers

To calculate the standard deviation of a sample, you divide the sum of squared deviations by ______.

n - 1 Signup and view all the answers

Match each company with their standard deviation ranking based on battery hours:

EverSoBright = Highest standard deviation Dependable = Medium standard deviation Beacon = Lowest standard deviation Signup and view all the answers

Given a sample with values {2, 4, 7, 12, 15}, what is the calculated standard deviation?

5.43 Signup and view all the answers

A higher standard deviation indicates that the data points are closer to the mean.

False Signup and view all the answers

What is the primary purpose of calculating standard deviation in statistical analysis?

To measure the dispersion or variability of a data set. Signup and view all the answers

What is the z-score for Raul's first test score of 72?

0.875 Signup and view all the answers

A z-score of 1.2 for a light bulb indicates that it has a lifespan shorter than the mean lifespan.

False Signup and view all the answers

What is the lifespan of the DuraBright Company's light bulb if its z-score is 1.2, with a mean of 842 hours and a standard deviation of 90?

950 hours Signup and view all the answers

The pth percentile is defined as the value for which p% of the data values are _____ than x.

less Signup and view all the answers

Match the following z-scores with their corresponding interpretation:

z = 0 = Score is at the mean z < 0 = Score is below the mean z > 0 = Score is above the mean z = 1 = Score is one standard deviation above the mean Signup and view all the answers

Which of the following statements is true about percentiles?

The 75th percentile indicates that 75% of the data is below this point. Signup and view all the answers

In a distribution, if the mean and median are the same, the distribution is symmetrical.

True Signup and view all the answers

In 2021, the median annual salary for physical therapists was $74,480. What percent of physical therapists earn more than this amount?

50% Signup and view all the answers

What is the standard deviation of the sample consisting of the numbers 2, 4, 7, 12, and 15?

5.43 Signup and view all the answers

Variance is the square root of the standard deviation.

False Signup and view all the answers

What is the mean of the sample set consisting of the numbers 2, 4, 7, 12, and 15?

8 Signup and view all the answers

The variance is calculated by taking the ______ of the standard deviation.

square Signup and view all the answers

Match each term to its correct definition:

Standard Deviation = Measure of dispersion Variance = Square of the standard deviation Deviation = Difference from the mean Population = Entire group being studied Signup and view all the answers

Which type of argument uses specific examples as premises to propose a general conclusion?

Inductive Signup and view all the answers

An argument is valid if its conclusion is guaranteed under its given set of premises.

True Signup and view all the answers

What is the conclusion in the deductive argument: 'All humans are mortal. Socrates is a human. Therefore, Socrates is mortal.'?

Socrates is mortal. Signup and view all the answers

An argument is __________ if it is not valid.

invalid Signup and view all the answers

Match the following example with its type of argument:

Example 1: I ate pizza and got a stomach ache. I ate pasta and got a stomach ache. Conclusion: Therefore, eating Italian food gives me stomach aches. = Inductive Example 2: All mammals have a heart. A dog is a mammal. Therefore, a dog has a heart. = Deductive Signup and view all the answers

What defines a deductive argument?

It draws a specific conclusion from general premises. Signup and view all the answers

All arguments presented are valid if the conclusion does not follow from the premises.

False Signup and view all the answers

What is the formula for calculating the range of a data set?

R = MAX - MIN Signup and view all the answers

Classify the argument: 'All spicy foods give me indigestion. Chili is a spicy food. Therefore, chili gives me indigestion.'

Deductive Signup and view all the answers

The standard deviation is always less than the range of a data set.

False Signup and view all the answers

What does a larger standard deviation indicate about a data set?

The data points are more spread out from the mean. Signup and view all the answers

To calculate the standard deviation of a sample, we use the symbol _____ to represent it.

s Signup and view all the answers

Match the statistical terms with their definitions:

Range = The difference between the maximum and minimum values Standard Deviation = A measure of dispersion based on the mean Variance = The average of the squared deviations from the mean Mean = The average value of a data set Signup and view all the answers

Why is the sum of the deviations from the mean always zero?

Because deviations can be both negative and positive. Signup and view all the answers

The range provides a complete measure of the dispersion of data in all cases.

False Signup and view all the answers

In statistical terms, what does the symbol σ represent?

The standard deviation of a population. Signup and view all the answers

What is the sum of all deviations from the mean for any data set?

It is equal to zero Signup and view all the answers

The sample standard deviation is designated by the symbol s.

True Signup and view all the answers

What is the standard deviation of the sample calculated from the numbers 2, 4, 7, 12, and 15?

5.43 Signup and view all the answers

The average of a set of numbers is also known as the __________.

mean Signup and view all the answers

Match each company to its standard deviation ranking of their battery hours:

EverSoBright = Lowest standard deviation Dependable = Medium standard deviation Beacon = Highest standard deviation Signup and view all the answers

In calculating the standard deviation, which value do you divide the sum of squared deviations by when working with a sample of n numbers?

n - 1 Signup and view all the answers

Variance is a statistic that is used to measure the central value of a dataset.

False Signup and view all the answers

What statistical measure is used to represent the average squared deviations from the mean?

variance Signup and view all the answers

What is the first step in finding quartiles in a data set?

Rank the data Signup and view all the answers

The first quartile, Q1, is the median of the data values that are greater than Q2.

False Signup and view all the answers

What is the formula to calculate the percentile of a score x?

Number of data values less than x / Total number of data values * 100 Signup and view all the answers

In a normal distribution, a z-score of ______ indicates that a data point is above the mean.

positive Signup and view all the answers

Match the following quartile definitions with their respective terms:

Q1 = Median of the lower half of the data Q2 = Median of the entire data set Q3 = Median of the upper half of the data Interquartile Range = Difference between Q3 and Q1 Signup and view all the answers

If the 25th percentile for the annual salary of a police dispatcher is $32,761, what percentage of dispatchers earn less than this amount?

25% Signup and view all the answers

For the given data set of weights, the quartile values can be determined by simply averaging all values.

False Signup and view all the answers

What is the value of the second quartile, Q2, in a ranked set of data?

Median of the data Signup and view all the answers

What is the standard deviation of the sample consisting of the numbers 2, 4, 7, 12, and 15?

5.43 Signup and view all the answers

Variance is the square root of the standard deviation.

False Signup and view all the answers

What is the variance of the sample if the standard deviation is 5.43?

29.49 Signup and view all the answers

To calculate the variance of a sample, you divide the sum of squared deviations by __________.

n - 1 Signup and view all the answers

Match the following terms with their definitions:

Standard Deviation = A measure of dispersion that indicates how much data points deviate from the mean Variance = The square of the standard deviation Mean = The average of a set of numbers Deviation = The difference between a data point and the mean Signup and view all the answers

What is the formula for calculating variance?

Variance = Standard Deviation^2 Signup and view all the answers

The standard deviation can be defined as the square of the variance.

False Signup and view all the answers

If the standard deviation of a dataset is 4, what is the variance?

16 Signup and view all the answers

The z-score for a given data value x indicates how many __________ from the mean the data point is.

standard deviations Signup and view all the answers

Match the given standard deviation with its variance:

3 = 9 5 = 25 7 = 49 10 = 100 Signup and view all the answers

Which team demonstrates the least variation in player heights from the mean?

Team A Signup and view all the answers

A higher standard deviation indicates that data points are more spread out from the mean.

True Signup and view all the answers

Calculate the variance of a sample with a standard deviation of 10.

100 Signup and view all the answers

In the argument represented symbolically by ~p → r, what does ~p signify?

She did not get on the plane Signup and view all the answers

The conclusion of an argument is invalid if it is true when all premises are true.

False Signup and view all the answers

What is represented by the symbol ∴ in logical arguments?

Therefore Signup and view all the answers

In symbolic logic, the statement 'Aristotle was human' is represented by the variable ______.

h Signup and view all the answers

Match each component of the argument to its appropriate description:

h = Aristotle was human m = Aristotle was mortal ~p = She did not get on the plane r = She will regret it Signup and view all the answers

Which of the following represents the second premise in the argument about Aristotle's mortality?

h Signup and view all the answers

Constructing a truth table is unnecessary when determining the validity of an argument.

False Signup and view all the answers

If the premises are true and the conclusion is false, the argument is considered ______.

invalid Signup and view all the answers

What is the median of the list 46, 23, 92, 89, 77, 108?

83 Signup and view all the answers

The mode is defined as the number that appears most frequently in a data set.

True Signup and view all the answers

What is the weighted mean of a student's scores if the weights of the scores are 1, 1, 1, and 2 for the final exam?

The weighted mean depends on the actual scores of the tests and the final exam. Signup and view all the answers

In a data set, if every number occurs only once, there is __________.

no mode Signup and view all the answers

What is the mode of the list 18, 15, 21, 16, 15, 14, 15, 21?

15 Signup and view all the answers

Match the following measures of central tendency with their definitions:

Mean = The average of a set of numbers Median = The middle value when numbers are sorted Mode = The number that occurs most frequently Weighted Mean = An average that takes into account the relative importance of values Signup and view all the answers

The median is always the middle number in a dataset with an odd number of entries.

True Signup and view all the answers

How is the median calculated in a data set with an even number of entries?

By averaging the two middle numbers after sorting the data set. Signup and view all the answers

What is the value of the first quartile (Q1) in the data set: 2, 5, 5, 8, 11, 12, 19, 22, 23, 29, 31, 45, 83, 91, 104, 159, 181, 312, 354?

11 Signup and view all the answers

The median is considered the first quartile in a data set.

False Signup and view all the answers

What is the formula to calculate a percentile for a score?

Number of data values less than x divided by total number of data values multiplied by 100 Signup and view all the answers

In a data set, the _______ divides the ranked data into four equal parts.

quartiles Signup and view all the answers

Match each statistic with its definition:

Q1 = First quartile Q2 = Median Q3 = Third quartile Percentile = Value below which a certain percentage of data falls Signup and view all the answers

If Roland received a z-score of 0.6 with a mean score of 65.5, what can be inferred about his test score of 70?

It is above average. Signup and view all the answers

The third quartile (Q3) represents the median of the upper half of the data values.

True Signup and view all the answers

What is the 25th percentile in relation to a data set?

The value below which 25% of the data falls. Signup and view all the answers

What is the symbolic form of the argument presented?

a→f, f→p, ∴a→p Signup and view all the answers

The argument is valid based on the truth table provided.

True Signup and view all the answers

What are the symbols used for 'I arrive before 8 A.M.' and 'I will make the flight'?

a and f Signup and view all the answers

If I make the flight, then I will give the __________.

presentation Signup and view all the answers

Match the premises to their logical implications:

a → f = If I arrive before 8 A.M., then I will make the flight. f → p = If I make the flight, then I will give the presentation. a → p = If I arrive before 8 A.M., then I will give the presentation. Signup and view all the answers

Which row in the truth table indicates a false conclusion?

Row 2 Signup and view all the answers

The premises a → f and f → p lead to the conclusion a → p.

True Signup and view all the answers

What does the conclusion a → p symbolize in the argument?

If I arrive before 8 A.M., then I will give the presentation. Signup and view all the answers

In the symbolic form of the argument, 'If she doesn’t get on the plane, she will regret it. She doesn’t regret it. Therefore, she got on the plane,' what does ~p represent?

She did not get on the plane. Signup and view all the answers

The conclusion of an argument is considered valid if it is true in every row of the truth table where all premises are true.

True Signup and view all the answers

What is the symbolic form of the argument 'If it rains, then the game will not be played. It is not raining. Therefore, the game will be played'?

~r → ~g, ~r, ∴g Signup and view all the answers

In logical expressions, the three dots ∴ represent __________.

therefore Signup and view all the answers

Match the terms to their meanings:

h = Aristotle was human m = Aristotle was mortal ~p = She did not get on the plane ∴ = Therefore Signup and view all the answers

Which of the following statements expresses the first premise in the argument involving Aristotle?

h m Signup and view all the answers

A truth table must be constructed for every argument to assess its validity.

True Signup and view all the answers

What is the logical conclusion drawn from the premises, 'If it rains, then the game will not be played. It is not raining.'?

The game will be played. Signup and view all the answers

Which type of reasoning is exemplified by the argument: If it is raining, then the grass is wet. It is not raining. Therefore, the grass is not wet?

Fallacy of inverse Signup and view all the answers

An argument is valid if its conclusion follows from the premises.

True Signup and view all the answers

What is the conclusion of the argument: 'If you helped solve the crime, then you should be rewarded. You helped solve the crime. Therefore, you should be rewarded.'?

You should be rewarded. Signup and view all the answers

The argument structure 'c→s, s, ∴c' is identified as the __________.

fallacy of converse Signup and view all the answers

Match each argument with its type of reasoning:

g→h, ~g, ∴~h = Fallacy of inverse h→r, h, ∴r = Direct reasoning c→s, s, ∴c = Fallacy of converse i∨w, ~i, ∴w = Disjunctive reasoning Signup and view all the answers

Which argument is an example of disjunctive reasoning?

The argument is of the form i∨w, ~i, ∴w. Signup and view all the answers

The argument 'If you helped solve the crime, then you should be rewarded. You should be rewarded. Therefore, you helped solve the crime.' is valid.

False Signup and view all the answers

Identify whether the argument 'If the movie’s production costs exceed $50 million, then I want to see it. The production costs were less than $50 million. Therefore, I do not want to see it.' is valid or invalid.

Invalid Signup and view all the answers

What does the Greek letter sigma (Σ) signify in statistics?

Summation of a set of numbers Signup and view all the answers

The mode is the value that occurs most frequently in a data set.

True Signup and view all the answers

What symbol is used to denote the mean of a sample?

x bar Signup and view all the answers

The __________ is the middle number in a ranked list of data.

median Signup and view all the answers

Match the following statistical terms with their definitions:

Arithmetic Mean = Sum of values divided by the count Median = Middle value in a sorted list Mode = Most frequently occurring value Population = Entire group being studied Signup and view all the answers

Which of the following statements is true regarding sample and population means?

Population mean is denoted by μ, while sample mean is denoted by x bar Signup and view all the answers

The median can be found by ranking the numbers and selecting the highest value.

False Signup and view all the answers

What is the meaning of the symbol μ in statistics?

Mean of the population Signup and view all the answers

Which form of reasoning can be applied to the argument: 'If I have a cold, then I find it difficult to sleep. I find it difficult to sleep. ∴ I have a cold.'?

Invalid Argument Signup and view all the answers

The argument 'The program is interesting, or I will watch the basketball game. The program is not interesting. ∴ I will watch the basketball game' is valid.

True Signup and view all the answers

What can be concluded from the premises 'If they eat (f), they will go back (b)' and 'If they go back (b), they will have a party (p)'?

If they eat, they will have a party. Signup and view all the answers

If the argument structure is p → q, and q is true, then the conclusion drawn is ______.

invalid Signup and view all the answers

Match the following logical forms with their validity:

p → q, q, ∴ p = Invalid p → q, p, ∴ q = Valid p ∨ q, ~p, ∴ q = Valid p → q, ~q, ∴ ~p = Valid Signup and view all the answers

Which type of reasoning uses the form p ∨ q?

Disjunctive Reasoning Signup and view all the answers

The Fallacy of the Inverse involves the form p → q leading to ∴ ~p.

True Signup and view all the answers

Identify the premises in the argument: 'If you can dream it (p), you can do it (q). You can dream it (p).'

p: You can dream it; q: You can do it. Signup and view all the answers

Study Notes

Z-Score

Z-score is a standardized score that tells us how many standard deviations a data point is from the mean.
Formula: Z = (x-μ)/σ for population and Z = (x-x̄)/s for sample.
Z-score helps compare data points from different distributions.

Example 1

Raul scored 72 on a test with a mean of 65 and standard deviation of 8.
His Z-score is 0.875.
Raul scored 60 on another test with a mean of 45 and standard deviation of 12.
His Z-score is 1.25.
Raul performed better on the second test compared to other students.

Example 2

A consumer group tested 100 light bulbs, finding a mean life of 842 hours and a standard deviation of 90 hours.
One bulb had a Z-score of 1.2.
Plugging Z-score into the formula, we find the bulb had a lifespan of 950 hours.

Percentiles

A percentile is a value below which a certain percentage of data points fall.
Example: The 90th percentile for physical therapist salaries means 90% of physical therapists earn less than that salary.
Median is the 50th percentile.
To find the percentile of a single data point, divide the number of data points below that value by the total number of data points, then multiply by 100.

Standard Deviation

Standard deviation measures how spread out data points are from the mean.
It uses the sum of squared deviations from the mean.
Sample standard deviation (s) is used when working with a subset of data, while population standard deviation (σ) is for the entire population.

Calculating Standard Deviation

Step 1: Find the mean of the data set.
Step 2: Calculate the deviation of each data point from the mean.
Step 3: Square each deviation and sum them.
Step 4: Divide the sum of squared deviations by (n-1) for a sample, where n is the sample size.
Step 5: Take the square root of the result from Step 4.

Example 3

A consumer group tested 8 batteries from 3 different companies.
The standard deviation for each company's batteries helps determine which company produces batteries with the most consistent performance.

Variance

Variance is another measure of dispersion, calculated as the square of the standard deviation.
It is also used to understand the spread of data points around the mean.

Frequency Distribution

A frequency distribution table lists observed events and the number of times they occur.
It helps organize raw data and provides a clearer picture of the data's frequency distribution.

Arguments in Symbolic Form

An argument consists of a series of statements that lead to a conclusion
Arguments can be written in symbolic form to make their logic easier to see
An argument is valid if the conclusion is true whenever all the premises are assumed to be true
An argument is invalid if it is not a valid argument

Types of Arguments

Inductive argument: Uses specific examples to make a general conclusion (from specific to general)
Deductive argument: Uses general statements to make a specific conclusion (from general to specific)

Measures of Dispersion

Range (R) measures the difference between the maximum and minimum value in a data set
Standard deviation is a measure of dispersion that uses the amount by which each individual data value deviates from the mean and is less sensitive to extreme values
Variance for a given set of data is the square of the standard deviation

Percentiles and Quartiles

Percentiles divide a data distribution into equal groups, with a single value representing the percentage of scores that fall below a certain point
Quartiles divide a ranked data set into four equal groups, with three specific values (Q1, Q2, Q3) representing the division points

Arguments and Truth Tables

Arguments can be represented symbolically.
Each premise is a statement that is accepted as true.
The conclusion is a statement that is supposed to be true based on the premises.
A truth table is used to determine the validity of an argument.
If the conclusion is true in every row of the truth table in which all the premises are true, then the argument is valid.

The Median

The middle number in an ordered set of data is called the median.
For an even number of data points, the median is the average of the two middle numbers.

The Mode

The mode is the data point that appears most often in a set of data.
A set of data may have no mode or multiple modes if multiple data points appear the same number of times.

The Weighted Mean

Some data values may be more important than others, requiring weighted means.
Weights are assigned to each data value, and the sum of each data value multiplied by its weight is divided by the sum of the weights.

Standard Deviation

Measures the amount of variation or dispersion of a set of data values from their mean.
A higher standard deviation indicates a greater amount of variation.

Variance

The square of the standard deviation.
A larger variance indicates greater variation in the data.

Z-score

Represents how many standard deviations a data point is away from the mean.
A z-score of 0 indicates the data point is equal to the mean.

Percentiles

Indicate the percentage of data points in a set that fall below a certain data value.
For a data set with n data points, the pth percentile is the value that has p percent of the data points below it.
For a data set, the percentile rank for a data point x is the percentage of data points in the set that are less than or equal to x.

Quartiles

The three values that partition a ranked data set into four (approximately) equal groups.
The second quartile is the median of the data set.
The first quartile is the median of the data values less than the second quartile.
The third quartile is the median of the data values greater than the second quartile.

Arguments and Truth Tables

Arguments can be shown to be valid if they have the same symbolic form as an argument that is known to be valid.
The three dots ∴ are a symbol for "therefore".

The Median

Another type of average is the median.
The median is the middle number or the mean of the two middle numbers in a list of numbers that have been arranged in numerical order from smallest to largest or largest to smallest.

The Arithmetic Mean

The Arithmetic Mean is a measure of central tendency.
Statisticians often collect data from small portions of a large group to determine information about the group.
The entire group under consideration is known as the population, and any subset of the population is called a sample.
It is traditional to denote the mean of a sample by (which is read as “x bar”) and to denote the mean of a population by the Greek letter (lowercase mu).
The traditional symbol used to indicate a summation is the Greek letter sigma, .
The notation x, called summation notation, denotes the sum of all the numbers in a given set.
The mean can be defined using summation notation.
The arithmetic mean is the sum of all values divided by the number of values.

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