STAT/MATH 3379 Elementary Statistics: Chapter 3 - Averages and Variation

Flashcards covering z-scores, percentiles, quartiles, interquartile range, outlier detection, and box-and-whisker plots from Chapter 3: Averages and Variation.

What does a z-score represent in statistics?

It represents how many standard deviations a value is from its population mean.

What is the formula for calculating a z-score?

z = (x - μ) / σ, where x is the value, μ is the population mean, and σ is the population standard deviation.

If a man's height has a z-score of 1.16 and a woman's height has a z-score of 1.50, who is relatively taller compared to their respective gender populations?

The woman is relatively taller because her z-score (1.50) is higher than the man's (1.16), indicating she is more standard deviations above her gender's mean height.

What do percentiles divide a data set into?

Percentiles divide a data set into hundredths.

What does the pth percentile indicate?

It separates the lowest P% of the data from the highest (100 – p)%.

Does a raw score of 95 out of 100 on an exam automatically mean you are at the 95th percentile?

No, the percentile indicates relative position. If only 80% of the scores fell at or below yours, you would be at the 80th percentile even with a raw score of 95.

How do quartiles divide a data set?

Quartiles divide a data set into four approximately equal pieces.

What do Q1, Q2, and Q3 represent?

Q1 (first quartile) separates the lowest 25% of data. Q2 (second quartile) is the median, separating the lowest 50%. Q3 (third quartile) separates the lowest 75% of data.

What is the Interquartile Range (IQR) and how is it calculated?

IQR is a measure of variation representing the range of the middle half of the data, calculated as IQR = Q3 – Q1.

How is the Lower Outlier Boundary calculated?

Lower Outlier Boundary = Q1 – 1.5(IQR).

How is the Upper Outlier Boundary calculated?

Upper Outlier Boundary = Q3 + 1.5(IQR).

When is a data value considered an outlier?

A data value is considered an outlier if it is less than the lower outlier boundary or greater than the upper outlier boundary.

What 'five-number summary' is required to create a box-and-whisker plot?

The five-number summary includes the Minimum, First quartile (Q1), Median (Q2), Third quartile (Q3), and Maximum values.

What is the main purpose of a box-and-whisker plot?

It highlights important features of a data set using the five-number summary and visually represents its distribution.