Section 3 4 MEASURE OF RELATIVE STANDING AND

Section 3. 4 MEASURE OF RELATIVE STANDING AND BOXPLOTS

Z - SCORE The number of standard deviations a given number, x, is from the mean.

SAMPLE Z - SCORE X is the value S is the sample standard deviation is the sample mean

PROPORTION Z - SCORE X is the value σ is the sample standard deviation μ is the sample mean

EXAMPLE When Steve Jobs was CEO of Apple, he earned an annual salary of $1. The CEO of the 50 largest US companies had a mean salary of $1, 449, 779 and a standard deviation of $527, 651 What is the difference between Jobs' salary and the mean CEO salary?

EXAMPLE How many standard deviations is Jobs' salary form the mean?

EXAMPLE Is this an usual or unusual salary?

INTERPRETING Z-SCORES

PERCENTILES Method to divide the set of data. P 1 is the first percentile P 99 is the 99 th percentile How?

EXAMPLE Given the following duration times (seconds) of 24 eruptions of the Old Faithful Geyser in Yellowstone National Park 110, 120, 178, 213, 234, 235, 237, 240, 243, 245, 250, 251, 252, 254, 255, 259, 260, 266, 269, 273

EXAMPLE Find the percentile corresponding to 213 sec.

EXAMPLE Find the time for P 60.

EXAMPLE Find the time for P 85.

QUARTILE Breaking the data set into quarters.

QUARTILE Breaking the data set into quarters.

QUARTILE vs PERCENTILE First Quartile = P 25 Second Quartile = P 50 = Median Third Quartile = P 75

EXAMPLE Given the following duration times (seconds) of 24 eruptions of the Old Faithful Geyser in Yellowstone National Park 110, 120, 178, 213, 234, 235, 237, 240, 243, 245, 250, 251, 252, 254, 255, 259, 260, 266, 269, 273

EXAMPLE Find the time for Quartile 1

EXAMPLE Find the time for Q 3

BOXPLOT BOX AND WHISKER DIAGRAM A graph that consists of a line extending from the minimum value to the maximum value, and a box with lines drawn at the first quartile Q 1, the median, and the third quartile Q 3.

SKEWED BOXPLOTS

STEPS TO CONSTRUCT A BOXPLOT List the values in increasing order Find the 5 -number summary Minimum Value First Quartile = Q 1 = P 25 Second Quartile = Q 2 = P 50 = median Third Quartile = Q 3 = P 75 Maximum Value Construct a rectangle around Q 1, Q 2 and Q 3 Draw line extending to the min and max value

EXAMPLE Given the following duration times (seconds) of 24 eruptions of the Old Faithful Geyser in Yellowstone National Park 110, 120, 178, 213, 234, 235, 237, 240, 243, 245, 250, 251, 252, 254, 255, 259, 260, 266, 269, 273 Construct a Boxplot Is it skewed?