Download Quiz 2.3-2.4

Sections 2.3 and 2.4
Quiz 2.3 – 2.4 tomorrow
(or next school day)
-May use 1 side of a 4 x 6 note
card for the quiz
Percentiles and Cumulative
Relative Frequency Plots
Percentiles measure position within a data
set.
Percentiles and Cumulative
Relative Frequency Plots
Percentiles measure position within a data
set.
Q1 is 25th percentile - - the value that
separates the lowest 25% of the ordered
values from the rest
Median is ______ percentile
Percentiles and Cumulative
Relative Frequency Plots
Percentiles measure position within a data
set.
Q1 is 25th percentile - - the value that
separates the lowest 25% of the ordered
values from the rest
Median is 50th percentile
Q3 is the _____ percentile
Percentiles and Cumulative
Relative Frequency Plots
Percentiles measure position within a data
set.
Q1 is 25th percentile - - the value that
separates the lowest 25% of the ordered
values from the rest
Median is 50th percentile
Q3 is the 75th percentile
Percentiles and Cumulative
Relative Frequency Plots
In general, a value is at the kth
percentile if k% of all values are
less than or equal to it.
Suppose you have a set of univariate data
(data that involves a single variable per
case).
The data consists of the weights of the
students in a class.
What are the cases?
What is the variable?
Suppose you have a set of univariate data
(data that involves a single variable per
case).
The data consists of the weights of the
students in a class.
What are the cases? Individual students
What is the variable?
Suppose you have a set of univariate data
(data that involves a single variable per
case).
The data consists of the weights of the
students in a class.
What are the cases? Individual students
What is the variable? The weight for each
student
The data consists of the weights of the
students in a class.
List all the measures you know to describe
the data set.
Hint: Should list 11 measures
List all the measures you know to describe
the data set.
x, sx, median, Q1, Q3, min, max, range, IQR,
mode, and outliers
List all the measures you know to describe
the data set.
x, sx, median, Q1, Q3, min, max, range, IQR,
mode, and outliers
Now categorize these measures in terms
of describing shape, center, or spread.
List all the measures you know to describe
the data set.
x, sx, median, Q1, Q3, min, max, range,
IQR, mode, and outliers
Now categorize these measures in terms of
describing shape, center, or spread.
None of these alone describe the shape.
How do you describe the shape?
How do you describe the shape?
•
•
•
•
uniform
normal distribution
skewed left or right
bimodal
Page 80, P28
P28 (Rescaling)
(a) converting height from inches to feet is
rescaling
Which measures are affected by rescaling?
P28 (Rescaling)
(a) converting height from inches to feet is
rescaling
Which measures are affected by rescaling?
• mean
• median
• standard deviation
• and IQR
P28 (Rescaling)
(a) Divide each of the summary statistics by
12 so:
• the mean is
P28 (Rescaling)
(a) Divide each of the summary statistics by
12 so:
• the mean is 4 feet
• the standard deviation is
P28 (Rescaling)
(a) Divide each of the summary statistics by
12 so:
• the mean is 4 feet
• the standard deviation is 0.2 foot
• the median is
P28 (Rescaling)
(a) Divide each of the summary statistics by
12 so:
• the mean is 4 feet
• the standard deviation is 0.2 foot
• the median is 3.75 feet and
• the IQR is
P28 (Rescaling)
(a) Divide each of the summary statistics by
12 so:
• the mean is 4 feet
• the standard deviation is 0.2 foot
• the median is 3.75 feet and
• the IQR is 0.25 foot
P28
(b) each child growing 2 inches is
____________
P28 (Recentering)
(b) each child growing 2 inches is
recentering
P28 (Recentering)
(b) each child growing 2 inches is
recentering
Which measures are affected by
recentering?
P28 (Recentering)
(b) each child growing 2 inches is
recentering
Which measures are affected by
recentering?
Only the centers:
• mean
• median
P28 (Recentering)
(b) Add 2 to the measures of the center so
• mean is 50 inches
• median is 47 inches
Recentering does not change the spread so
• standard deviation stays 2.4 inches
• IQR stays 3 inches
P28 (Recentering and Rescaling)
(c) each child growing 4 inches is
recentering and converting heights to feet
is rescaling.
P28 (Recentering and Rescaling)
(c)
P28 (Recentering and Rescaling)
(c)
Plot this data into a stem-and-leaf plot:
23, 125, 8, 23, 50
Plot this data into a stem-and-leaf plot:
23, 125, 8, 23, 50
0
2
5
12
8
3 3
0
5
Plot this data into a stem-and-leaf plot:
23, 125, 8, 23, 50
0
2
5
12
8
3 3
0
5
5 0 represents 50
Page 69, P15
P15
The new mean height will be about 4 feet 4
inches.
x = [5(4) + 6]÷ 6
P15
The new mean height will be about 4 feet 4
inches.
The median will not change because it will
still be one of the heights of the 3rd graders,
who all are about 4 feet tall.
4 4 4 4 4 6
Page 70, P21
Use calculator to find (a) 5-number summary
and (e) to draw a modified boxplot.
Also answer (b), (c), and (d),
P21
P21
P21
Page 72, E33
• Enter Predator data in List 1
• Enter NonPredator data in List 2
Page 72, E33
• Enter Predator data in List 1
• Enter NonPredator data in List 2
• Use L1 for Plot 1 and L2 for Plot 2 to
display both modified boxplots on same
screen
E33
Page 73, E43
Page 73, E43
Enter Weights in List 1
Enter Frequency in List 2
E43
Page 81, E53
Page 81, E53
a. Median: 23 or 24 cents.
To estimate this, find the amount of change
that corresponds to the 50th percentile
Page 81, E53
a. Median: 23 or 24 cents.
To estimate this, find the amount of change
that corresponds to the 50th percentile
b. Q1 ≈ 10 cents and Q3 ≈ 70 cents.
Q1 corresponds to 25th percentile and Q3
corresponds to 25th percentile
IQR = 60 cents
E53
Page 82, E54
E54
Page 82, E57
E57
Questions?