Transcript box and whisker

Activator
Look at the #s and the graph
•
Can you determine what the dots
represent?
31, 31, 32, 32, 32, 32, 33, 33, 36
31
32
33
34
35
36
1.
Put the data in order from least to greatest
2. Find the median. (If there is an even set of
data, we will discuss that later)
3. The middle # is the median and all the numbers
below it make up the lower half. All the numbers
above it make up the upper half.
4. The median of both halves is the quartile
5. The smallest # and the largest # are your
extremes.
Vocabulary
• Interquartile Range: The difference
between the Upper Quartile and the Lower
• Quartile.
31
•
32
33
34
35
36
31, 31, 32, 32, 32, 32, 33, 33, 36
1. Find the lower and upper extremes
2. Find the median
3. Find the lower half and the upper half
4. Find the lower quartile and the upper quartile.
Assessment Prompt
• 1’s: What are the extremes of the 5
number summary?
• 2’s: what are the quartiles and median of
the 5 number summary?
Once you have found the median, LQ, UQ, LE, and
UE, you need to plot them on a number line.
Write the 5 numbers down and decide how long
your number line needs to be. It must include the
smallest and largest value.
Now decide how you are going to count by on the
number line.
Draw your Box (use the median, LQ, and UQ)
Draw your whiskers (use the LE and UE)
Once you have found the median, LQ, UQ, LE, and
UE, you need to plot them on a number line.
Write the 5 numbers down and decide how long
your number line needs to be. It must include the
smallest and largest value.
Now decide how you are going to count by on the
number line.
Draw your Box (use the median, LQ, and UQ)
Draw your whiskers (use the LE and UE)
Assessment Prompt
• 1’s: What are the extremes of the 5
number summary?
• 2’s: what are the quartiles and median of
the 5 number summary?
3-2-1
• 3: what are the 3 values that make up the
box?
• 2: what are the 2 values that make up the
whiskers?
• 1: Explain the process for finding the 5 #
summary.
• Worksheet
Scatterplots
E.Q How do you construct and
interpret scatter plots?
What conclusions can you draw
from this scatter plot?
Things to know
• Similar to line graphs BUT DO NOT connect the
dots.
• Usually consists of a large body of data.
• Shows how much one variable effects the
other.
• Looking for a correlation (relationship) between
x and y.
• The closer the points are to making a straight
line, the higher/stronger the correlation ( A
straight line is a perfect correlation.)
Age vs. Years Left to Live
Years to live
52
44
36
28
20
0
30
40
50
Age
60
Height vs. Hours of Sleep
Hours of sleep
10
8
6
4
2
0
40
45
50
55
Height
60
65
70
Investigating Scatter Plots
Weight Loss Over Time
250
How shirts affect salary
200
500000
400000
Weight
150
Salary
Weight
100
50
300000
200000
100000
0
0
2
4
6
8
10
12
Da ys w orke d out pe r month
1
3
How Study Time Affects Grades
5
7
9
11
Shirts Owned
120
100
Overall grade
0
80
60
40
20
0
0
0.5
1
1.5
2
2.5
3
Time in hours
3.5
4
4.5
5
13
15
17
Investigating Scatter Plots
• Scatter plots are similar to line graphs in
that each graph uses the horizontal ( x )
axis and vertical ( y ) axis to plot data
points.
• Scatter plots are most often used to show
correlations or relationships among data.
Investigating Scatter Plots
• Positive correlations occur when two
variables or values move in the same
direction.
– As the number of hours that you study
increases your overall class grade increases
Investigating Scatter Plots –
Positive Correlation
How Study Time Affects Grades
120
Overall grade
100
80
60
40
20
0
0
0.5
1
1.5
2
2.5
3
Time in hours
3.5
4
4.5
5
Study
Time
Class
Grade
0
55
0.5
61
1
67
1.5
73
2
81
2.5
89
3
91
3.5
93
4
95
4.5
97
Investigating Scatter Plots
• Negative Correlations occur when
variables move in opposite directions
– As the number of days per month that you
exercise increases your actual weight
decreases
Investigating Scatter Plots –
Negative Correlation
Work out
time
Weight Loss Over Time
250
200
Weight
0
200
0.5
205
1
190
1.5
195
2
180
2.5
190
3
170
3.5
177
4
160
4.5
170
5
150
5.5
168
6
140
6.5
150
7
130
7.5
170
8
120
Weight
150
Weight
100
50
0
0
2
4
6
8
10
Days w orked out per month
12
Investigating Scatter Plots
• No correlation exists if there is no
noticeable pattern in the data
– There is no relationship between the number
of shirts someone owns and their annual
salary
Investigating Scatter Plots – No
Correlation
number of
shirts
owned
How does your wardrobe affect your
salary
80
Salary
60
40
20
0
0
10
20
30
Number of shirts owned
40
50
salary
1
1
2
0
3
50
4
30
5
25
6
17
7
2
8
40
9
8
10
25
11
12
12
7
13
19
14
55
15
71
http://mste.illinois.edu/courses/ci33
0ms/youtsey/scatterinfo.html
Assessment Prompt
• How do you determine the type of
correlation on a scatter plot?
Line of Best Fit
• A line of best fit is a line that best
represents the data on a scatter plot.
• A line of best fit may also be called a trend
line since it shows us the trend of the data
– The line may pass through some of the
points, none of the points, or all of the points.
– The purpose of the line of best fit is to show
the overall trend or pattern in the data and to
allow the reader to make predictions about
future trends in the data.
Use the data to create a scatter
plot
Total Fat (g)
(X)
Total Calories
(y)
Hamburger
9
260
Cheeseburger
13
320
Quarter Pounder
21
420
Quarter Pounder with Cheese
30
530
Big Mac
31
560
Arch Sandwich Special
31
550
Arch Special with Bacon
34
590
Crispy Chicken
25
500
Fish Fillet
28
560
Grilled Chicken
20
440
Grilled Chicken Light
5
300
Sandwich
Scatter Plot of the Data
Fat Grams and Calories in Food
700
Total Calories
600
500
400
300
200
100
0
0
5
10
15
20
25
Total Fat Grams
30
35
40
Things to remember
• A scatter plot with a positive correlation
has X and Y values that rise together.
• A scatter plot with a negative correlation
has X values that rise as Y values
decrease
• A scatter plot with no correlation has no
visible relationship
• The line of best fit is the line that best
shows the trend of the data
x
-6
-4
-3
-1
0
2
5
y
-2
-3
-1
-3
0
0
0
Which statement best describes the
relationship between average traffic volume
and average vehicle speed shown on the
scatter plot?
a. As traffic volume increases,
vehicle speed increases.
b. As traffic volume increases,
vehicle speed decreases.
c. As traffic volume increases,
vehicle speed increases at
first, then decreases.
d. As traffic volume increases,
vehicle speed decreases at
first, then increases.
Summarizer
• Write a sentence that connects each point
to the next. You may go in either direction.
Data
Line of best
fit
Correlation