Statistics Quiz 3 Flashcards

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Questions and Answers

What is the class midpoint of the first class in a frequency table of quantitative data, which is 0-4?

2.5

What does a z-score represent?

Represents the number of standard deviations an observation is from the mean.

What are quartiles?

Divide data sets in fourths.

As the magnitude of the z-score increases, what happens to the relative difference of the observation from the mean?

The relative difference of the observation from the mean increases. Signup and view all the answers

What does it mean when stated that the 10th percentile of the head circumference of males 3 to 5 months of age in a certain city is 41.0 cm?

10% of 3- to 5-month old males have a head circumference that is 41.0 cm or less. Signup and view all the answers

Is standard deviation resistant to extreme observations?

No, standard deviation is not resistant to extreme observations. Signup and view all the answers

When is the interquartile range preferred as a measure of dispersion?

When the data are skewed or have outliers. Signup and view all the answers

For a symmetric distribution, what can be said about the lengths of the whiskers?

The left whisker is the same length as the right whisker. Signup and view all the answers

In a distribution that is skewed right, where is the median located?

Left of center of the box. Signup and view all the answers

In a distribution that is skewed left, what can be said about the whiskers?

The left whisker is longer than the right whisker. Signup and view all the answers

In a boxplot, if the median is left of the center of the box and the right whisker is substantially longer than the left whisker, what can be said about the distribution?

The distribution is skewed right. Signup and view all the answers

What happens to the interquartile range as the spread of a data set increases?

The higher the interquartile range will be. Signup and view all the answers

Which boxplot will likely have a larger standard deviation: Boxplot I or Boxplot II?

Boxplot II appears to have a greater spread than Boxplot I. Signup and view all the answers

What is the difference between univariate data and bivariate data?

In univariate data, a single variable is measured on each individual; in bivariate data, two variables are measured on each individual. Signup and view all the answers

What does it mean to say that two variables are positively associated?

There is a linear relationship between the variables, and whenever the value of one variable increases, the value of the other variable increases. Signup and view all the answers

What does it mean to say that two variables are negatively associated?

There is a linear relationship between the variables, and whenever the value of one variable increases, the value of the other variable decreases. Signup and view all the answers

If r = ______, then a perfect negative linear relation exists between the two quantitative variables.

-1 Signup and view all the answers

True or false: Correlation implies causation.

False Signup and view all the answers

Why might the data points not have a linear relationship?

They do not lie mainly in a straight line. Signup and view all the answers

Study Notes

Class Midpoint

The class midpoint for the class 0-4 is 2.5, calculated by averaging the endpoints (0 + 4) / 2.

z-score

A z-score measures how many standard deviations an observation is from the mean, indicating its relative position within a dataset.

Quartiles

Quartiles divide a data set into four equal parts, helping to understand the distribution of the data.

Magnitude of z-score

An increasing z-score indicates a larger difference from the mean, suggesting that the observation is more extreme.

Interpretation of Percentiles

Being at the 10th percentile means that 10% of the population, in this case, 3- to 5-month-old males, have a head circumference of 41.0 cm or less.

Resistance to Extreme Observations

Standard deviation is sensitive to extreme values, whereas the interquartile range (IQR) remains unaffected.

Preferred Measures of Dispersion

The interquartile range is preferred for skewed data or data with outliers. Standard deviation, conversely, considers all data points in its calculation, making it useful for normal distributions.

Symmetric Distribution

In symmetric distributions, the length of the left and right whiskers in a boxplot is equal.

Skewed Right Distribution

In right-skewed distributions, the median is positioned left of the center of the box in a boxplot.

Skewed Left Distribution

For left-skewed distributions, the left whisker of a boxplot is longer than the right whisker.

Boxplot Analysis

In a boxplot, if the median is left of center and the right whisker is significantly longer, the distribution is skewed right.

Data Spread and IQR

A greater spread in data results in a higher interquartile range, indicating more variability.

Standard Deviation and Boxplots

Boxplot II has a greater spread than Boxplot I; therefore, it is likely to have a larger standard deviation.

Univariate vs. Bivariate Data

Univariate data examines one variable per individual, while bivariate data examines two variables for each individual, allowing for analysis of relationships.

Positive Association

Positive association between two variables indicates a direct linear relationship; as one variable increases, the other also increases.

Negative Association

Negative association indicates an inverse linear relationship; as one variable increases, the other decreases.

Perfect Negative Correlation

A correlation coefficient (r) of -1 signifies a perfect negative linear relationship between two quantitative variables.

Correlation and Causation

Correlation does not imply causation; two correlated variables do not necessarily influence each other.

Linear Relationship of Data Points

Data points lacking a linear relationship do not primarily align along a straight line, indicating variable interaction is non-linear.

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Description

Test your knowledge on key statistics concepts with these flashcards. This quiz covers topics such as class midpoints, z-scores, and quartiles. Perfect for reinforcing your understanding of statistics!