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Title: Measure of Relative Standing and Boxplots
Description: This is a class lecture about Measure of Relative Standing and Boxplots. You can learn about the following: • Basics of z Scores, Percentiles, Quartiles, and Boxplots • Measures of Position • Percentiles • Finding the Percentile of a Data Value • Converting from the kth Percentile to the Corresponding Data Value • Quartiles • Interquartile Range Formula • Semi-interquartile Range Formula • Midquartile Formula • 5-Number Summary • Boxplot
Description: This is a class lecture about Measure of Relative Standing and Boxplots. You can learn about the following: • Basics of z Scores, Percentiles, Quartiles, and Boxplots • Measures of Position • Percentiles • Finding the Percentile of a Data Value • Converting from the kth Percentile to the Corresponding Data Value • Quartiles • Interquartile Range Formula • Semi-interquartile Range Formula • Midquartile Formula • 5-Number Summary • Boxplot
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MEASURES OF
RELATIVE STANDING
AND BOXPLOTS
(Class Lecture in Statistics)
Part 7
3
...
•The most important concept is the z score
...
3
...
1 - 3
Z score
z Score
(or standardized value)
the number of standard deviations
that a given value x is above or
below the mean
3
...
1 - 5
Interpreting Z Scores
Whenever a value is less than the mean, its
corresponding z score is negative
Ordinary values:
–2 ≤ z score ≤ 2
Unusual Values:
z score < –2 or z score > 2
3
...
1 - 7
Percentiles
are measures of location
...
P99,
which divide a set of data into 100
groups with about 1% of the values
in each group
...
1 - 8
Finding the Percentile
of a Data Value
Percentile of value x =
number of values less than x
100
total number of values
3
...
1 - 10
Converting from the
kth Percentile to the
Corresponding Data Value
3
...
Q1
(First Quartile) separates the bottom
25% of sorted values from the top 75%
...
Q3
(Third Quartile) separates the bottom
75% of sorted values from the top 25%
...
1 - 12
Quartiles
The first quartile is the 25th percentile
Q1 P25
• The second quartile is the 50th percentile
Q 2 P50
• The third quartile is the 75th percentile
Q3 P75
3
...
1 - 14
Some Other Statistics
Interquartile Range (or IQR): Q3 – Q1
Semi-interquartile Range:
Midquartile:
Q3 + Q1
Q3 – Q1
2
2
10 - 90 Percentile Range: P90 – P10
3
...
3
...
3
...
1 - 18
Boxplots - Normal
Distribution
Normal Distribution:
Heights from a Simple Random Sample of Women
3
...
1 - 20
Calculator: Five Number
Summary
• Five Number Summary (from
website mathbits
...
1 - 21
Calculator: Five Number
Summary
• Go to STAT - CALC and
choose 1-Var Stats
3
...
3
...
1 - 24
Calculator: Boxplot
• CLEAR out the graphs under y = (or
turn them off)
...
(choose STAT, #1 EDIT and type in
entries)
3
...
Be
sure the plot is ON, the second box-and-whisker icon
is highlighted, and that the list you will be using is
indicated next to Xlist
...
1 - 26
Calculator: Boxplot
• To see the box-and-whisker plot, press ZOOM
and #9 ZoomStat
...
3
...
1 - 28
Title: Measure of Relative Standing and Boxplots
Description: This is a class lecture about Measure of Relative Standing and Boxplots. You can learn about the following: • Basics of z Scores, Percentiles, Quartiles, and Boxplots • Measures of Position • Percentiles • Finding the Percentile of a Data Value • Converting from the kth Percentile to the Corresponding Data Value • Quartiles • Interquartile Range Formula • Semi-interquartile Range Formula • Midquartile Formula • 5-Number Summary • Boxplot
Description: This is a class lecture about Measure of Relative Standing and Boxplots. You can learn about the following: • Basics of z Scores, Percentiles, Quartiles, and Boxplots • Measures of Position • Percentiles • Finding the Percentile of a Data Value • Converting from the kth Percentile to the Corresponding Data Value • Quartiles • Interquartile Range Formula • Semi-interquartile Range Formula • Midquartile Formula • 5-Number Summary • Boxplot