Download upper quartile

Bellwork
1. Order the test scores from least to
greatest: 89, 93, 79, 87, 91, 88, 92.
79, 87, 88, 89, 91, 92, 93
2. Find the median of the test scores.
89
Box-and-Whisker Plots
Section 11.2
Step 1 – Order Numbers
Step 1. Order the set of numbers from least to greatest
Step 2 – Find the Median
Step 2. Find the median. The median is the
middle number. If the data has two middle
numbers, find the mean of the two
numbers. What is the median?
Step 3 – Upper & Lower Quartiles
Step 3: Find the lower and upper
medians or quartiles. These are the
middle numbers on each side of the
median. What are they?
Step 4 – Draw a Number Line
Now you are ready to construct the
actual box & whisker graph. First
you will need to draw an ordinary
number line that extends far
enough in both directions to
include all the numbers in your
data:
Step 5 – Draw the Parts
Step 4: Locate the main median 12
using a vertical line just above your
number line:
Step 5 – Draw the Parts
Locate the lower median 8.5 and
the upper median 14 with similar
vertical lines:
Step 5 – Draw the Parts
Next, draw a box using the lower
and upper median lines as
endpoints:
Step 5 – Draw the Parts
Finally, the whiskers extend out to
the data's smallest number 5 and
largest number 20:
Step 6 - Label the Parts of a Box-and-Whisker
Plot
Lower Quartile Median
Lower Extreme
3
1
4
Upper Quartile
Upper Extreme
2
5
Name the parts of a Box-and-Whisker Plot
The lower fourth and upper fourth quarters are
represented by “whiskers” that extend to the minimum
(least) and maximum (greatest) values.
Data set: 85,92,78,88,90,88,89
78
Lower quartile
85
88
88
Median
89
90 92
Upper quartile
What are minimum and maximum values?
The table below summarizes a cat breeder’s
records for kitten litters born in a given year. You
can divide the data into four equal part using
quartiles.
Litter Size
2
3
4
5
6
Number of
Litters
1
6
8
11
1
You know that the median of a data set divides the
data into a lower half and an upper half. The median
of the lower half is the lower quartile, and the
median of the upper half is the upper quartile.
Kitten Data
Lower half
Upper half
233333344444444555555555556
Upper quartile: 5
Lower quartile: 3
median of upper half
median of lower half
Median: 4
You know that the median of a data set divides the
data into a lower half and an upper half. The median
of the lower half is the lower quartile, and the
median of the upper half is the upper quartile.
Kitten Data
Lower half
Upper half
233333344444444555555555556
Upper quartile: 5
Lower quartile: 3
median of upper half
median of lower half
Median: 4
What letter is the _____?
F
E
D
Lower half
Upper half
233333344444444555555555556
B
A
How do you know?
c
Importance
Why do we need to know how to display and analyze
data in box-and-whisker plots ?
*It helps you to interpret and represent data.
*It gives a visual representation of data.
Tell your partner which reason is most important to
you. You can use one of mine or one of your own.
p/s - volunteers
Bellwork
 Make a box-and-whisker plot that represents
the data.
Cat lengths (in inches): 16, 18, 20, 25, 17,
22, 23, 21
Find the lower and upper quartiles for the data
set.
1. Order the data from least to greatest.
2. Find the median.
3. Find the median of the lower half – lower quartile
4. Find the median of the upper half – upper quartile
I do
A. 15, 83, 75, 12, 19, 74, 21
12 15 19 21 74 75 83
Order the values.
lower quartile: 15
upper quartile: 75
How did I find the lower and upper quartiles?
Find the lower and upper quartiles for the data
set.
1. Order the data from least to greatest.
2. Find the median.
3. Find the median of the lower half – lower quartile
4. Find the median of the upper half – upper quartile
We do
B. 75, 61, 88, 79, 79, 99, 63, 77
61 63 75 77 79 79 88 99
lower quartile:
Order the values.
63 + 75
= 69
2
79 + 88
upper quartile:
= 83.5
2
Find the lower and upper quartiles for the data
set.
1. Order the data from least to greatest.
2. Find the median.
3. Find the median of the lower half – lower quartile
4. Find the median of the upper half – upper quartile
We do
A. 25, 38, 66, 19, 91, 47, 13
13 19 25 38 47 66 91
lower quartile: 19
upper quartile: 66
Order the values.
Find the lower and upper quartiles for the data
set.
1. Order the data from least to greatest.
2. Find the median.
3. Find the median of the lower half – lower quartile
4. Find the median of the upper half – upper quartile
You do
B. 45, 31, 59, 49, 49, 69, 33, 47
31 33 45 47 49 49 59 69
Order the values.
33 + 45
lower quartile:
= 39
2
49 + 59
upper quartile:
= 54
2
Additional Example 2: Making a Box-and-Whisker Plot
Use the given data to make a box-and-whisker plot.
21, 25, 15, 13, 17, 19, 19, 21
Step 1. Order the data from least to greatest. Then
find the minimum, lower quartile, median, upper
quartile, and maximum.
13 15 17 19 19 21 21 25
minimum: 13
15 + 17
lower quartile:
2
maximum: 25
= 16 upper quartile:
median:
19 + 19
2
= 19
21 + 21
2
= 21
I do (cont.)
Additional Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 2. Draw a number line and plot a point above
each value from Step 1.
13 15 17 19 19 21 21 25
12
14
16
18
20
22
24
26 28
I do (cont.)
Additional Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 3. Draw the box and whiskers.
13 15 17 19 19 21 21 25
12
14
16
18
20
22
24
26 28
We do
Check It Out! Example 2
Use the given data to make a box-and-whisker plot.
31, 23, 33, 35, 26, 24, 31, 29
Step 1. Order the data from least to greatest. Then
find the minimum, lower quartile, median, upper
quartile, and maximum.
23 24 26 29 31 31 33 35
minimum: 23
lower quartile:
maximum: 35
24 + 26
2
= 25 upper quartile:
median: 29 + 31 = 30
2
31 + 33
2
= 32
We do (cont.)
Check It Out! Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 2. Draw a number line and plot a point above
each value.
23 24 26 29 31 31 33 35
22
24
26
28
30
32
34
36 38
We do (cont.)
Check It Out! Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 2.
3. Draw a
the
box and
whiskers.
number
line
and plot a point above
each value.
23 24 26 29 31 31 33 35
22
24
26
28
30
32
34
36 38
Step 1. Order the data from least to greatest. Then find
the minimum, lower quartile, median, upper quartile, and
maximum.
Step 2. Draw a number line and plot a point above each
value.
Step 3. Draw the box and whiskers.
The box-and-whisker plot represents the lengths (in seconds) of the songs played by a rock band at a concert.
a. Find and interpret the range of the data.
b. b. Describe the distribution of the data.
c. c. Find and interpret the interquartile range of the data.
d. d. Are the data more spread out below Q1 or above Q3? Explain.
Step 1 Draw and label the
axes.
Describing the
Shape of a
Distribution
Step 2 Draw a bar to represent the frequency of each
interval. The data on the right of the distribution are
approximately a mirror image of the data on the left of the
distribution.
So, the distribution is symmetric.
Step 1: Make a frequency table using the described
intervals. Then use the frequency table to make a
histogram.
Choosing
Appropriate
Measures
Step2: Because most of the data are on the right and the tail of
the graph extends to the left, the distribution is skewed left. So,
use the median to describe the center and the five-number
summary to describe the variation.
Step3: Using the frequency table and the histogram, you can see
that most of the speeds are more than 45 miles per hour. So, most
of the motorists were speeding.
Because the data on the right of the distribution for the female
students are approximately a mirror image of the data on the left
of the distribution, the distribution is symmetric. So, the mean
and standard deviation best represent the distribution for female
students.
Because most of the data are on the left of the distribution for
the male students and the tail of the graph extends to the right,
the distribution is skewed right. So, the median and five-number
summary best represent the distribution for male students.
Comparing
Data
Distributions
The mean of the female data set is probably in the 30–39 interval,
while the median of the male data set is in the 10–19 interval. So,
a typical female student is much more likely to use emoticons
than a typical male student.
The data for the female students is more variable than the data
for the male students. This means that the use of emoticons
tends to differ more from one female student to the next.
Compare the
distributions
using their
shapes and
appropriate
measures of
center and
variation.
The table shows the results of a survey that asked men and women
how many pairs of shoes they own.
a. Make a double box-and-whisker plot that represents the data.
Describe the shape of each distribution.
Comparing
Data
Distributions
b. b. Compare the number of pairs of shoes owned by men to the
number of pairs of shoes owned by women.
c. c. About how many of the women surveyed would you expect
to own between 10 and 18 pairs of shoes?
The distribution for men is skewed right, and
the distribution for women is symmetric.
Solve for x
3, 6, 4, 10, x; the mean is 6.
Bellwork
13, 15, 17, x, 20, 21; The median is 18