4.2.k4
KU vs KS
The chart below is a record of the margin of victory
for the boys basketball teams during the 13 most
recent games.
Construct a two box and whisker plots to represent
the data.
K 24 3
10 19 13 -9 35 24 6 30 21 30 25
U
K 37 -11 21 15 -3 9 25 16 21 2 60 -26 42
S
Slide 1
4.2.k4
KU vs KS
K 24 3
10 19 13 -9 35 24 6 30 21 30 25
U
K 37 -11 21 15 -3 9 25 16 21 2 60 -26 42
S
Order the numbers.
KU
KS
Slide 2
4.2.k4
KU vs KS
In each set identify the median, upper quartile,
lower quartile, upper extreme, lower extreme.
KU
-9, 3, 6, 10, 13, 19, 21, 24, 24, 25, 30, 30, 35
KS
-26, -11, -3, 2, 9, 15, 16, 21, 21, 25, 37, 42, 60
Slide 3
KU vs KS
4.2.k4
In each set identify the median(Q2), upper quartile(Q3),
lower quartile(Q1), upper extreme, lower extreme.
KU
-9, 3, 6, 10, 13, 19, 21, 24, 24, 25, 30, 30, 35
27.5
8
KS
-26,-11,-3, 2, 9, 15, 16, 21, 21, 25, 37, 42, 60
-0.5
-20
-10
31
0
10
20
30
40
50
60
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Slide 4
KU vs KS
4.2.k4
In each set identify the median(Q2), upper quartile(Q3),
lower quartile(Q1), upper extreme, lower extreme.
KU
-9, 3, 6, 10, 13, 19, 21, 24, 24, 25, 30, 30, 35
27.5
8
KS
-26,-11,-3, 2, 9, 15, 16, 21, 21, 25, 37, 42, 60
-0.5
-20
-10
31
0
10
20
30
40
50
60
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Slide 5
KU vs KS
4.2.k4
If you drop the lowest margin of error for each team how
does that affect the mean, medain and mode.
KU
-9, 3, 6, 10, 13, 19, 21, 24, 24, 25, 30, 30, 35
KS
-26, -11, -3, 2, 9, 15, 16, 21, 21, 25, 37, 42, 60I
KU
After
KS
Before After
Mean
17.8
Median 21
19.9
22.5
Mean
16
19.5
Median 16
18.5
Mode
24,30
Mode
21
Before
24,30
21
Slide 6
KU vs KS
4.2.k4
Which central tendency was effected
by the change the most?
KU
After
KS
Before After
Mean
17.8
Median 21
19.9
22.5
Mean
16
19.5
Median 16
18.5
Mode
24,30
Mode
21
Before
24,30
21
Slide 7
Teaching Concept #1
4.2.k4
Box-and-Whisker Plots
Use the data to make a box and whisker plot.
3, 6, 7, 7, 2, 8, 3, 9, 11, 10, 9, 3, 4, 12, 2, 14, 7, 5, 10
• Order the data:
•
•
•
•
2,2,3,3,3,4,5,6,7,7,7,8,8,9,10,10,11,12,14
Find the median and the medians of the upper and lower halves:
3, 7, 10.
Check whether extremes are outliers.
Plot the five values (minimum, maximum and the three quartiles).
Draw the box and whiskers.
●●
0
●
5
●
10
●
15
20
Slide 8
Teaching Concept #2
4.2.k4
Calculate Mean, Median, and Mode
Use the data below.
2, 2, 3, 3, 3, 4, 5, 6, 7, 7, 7, 8, 8, 9, 10, 10, 11, 12, 14
Median – Middle number in ordered list or; if even number
of elements, average of two middle numbers. Thus, 7.
Mean – Sum of all elements divided by the number of
elements. Thus, 131/19 ≈ 6.9.
Mode – Element that occurs most often. Thus, 3 and 7.
●●
0
●
5
●
10
●
15
20
Slide 9
Teaching Concept #3
4.2.k4
Calculate Range and
Inter-Quartile Range
Use the data below.
2, 2, 3, 3, 3, 4, 5, 6, 7, 7, 7, 8, 8, 9, 10, 10, 11, 12, 14
Range – Maximum minus minimum. Thus, 14 - 2 = 12.
IQR – Difference in 3rd and 1st Quartiles.
Thus 10 - 3 = 7.
●●
0
●
5
●
10
●
15
20
Slide 10
Application
4.2.k4
Application
The scores on Carl’s test in algebra are 73,68,93,82,
and 79. His grade is assigned according to the mean
of his test scores. What is his current grade?
73 + 68 + 93 + 82 + 79 = 395
395 / 5 = 79
Slide 11
Concrete Example #1
4.2.k4
Effects of Outliers
Find the mean, median, mode, range, and IRQ.
Step 1: Order the data 68, 73, 79, 82, 93.
Step 2: Find the median and the medians of the upper and
lower halves. Median - 79, Lower Quartile - 70.5,
Upper Quartile - 87.5.
Step 3: Check for outliers. No outliers right now.
Step 4:Plot the five and draw the box and whisker plot.
● ●
60
70
●
80
●
●
90
100 Slide 12
Concrete Example #1
4.2.k4
Effects of Outliers
Make a box and whisker plot for Carl’s scores –
73,68,93,82, & 79
Step 1: 68, 73, 79, 82, 93
Step 2: Median – 79
Lower Quartile – 70.5
Upper Quartile – 87.5
Step 3: No outliers
Step 4: Draw the plot.
● ●
60
70
●
80
Mean = 395/5 = 79
Median = 79
No mode
Range = 93 - 68 = 25
IQR = 87.5 – 70.5 = 17
●
●
90
100 Slide 13
Concrete Example #2
4.2.k4
Effects of Outliers
Carl was absent the day they took the last test. If he
doesn’t make it up, how would a zero affect his grade?
Recreate the box and whisker plot adding in the zero on his test.
Step 1: 0, 68, 73, 79, 82, 93
Step 2: Median - 76
Lower Quartile – 36.5
Upper Quartile – 86
Step 3: Yes, 0 is an outlier
Step 4: Draw the plot.
●
0
●
25
●
50
75
● ●
100
Slide 14
Concrete Example #2
4.2.k4
Effects of Outliers
Find the mean, median, mode, range, and IQR.
Mean = 395/6 = 65.8
Median = 76
No mode
Range = 93 – 0 = 93
IQR = 86 – 36.5 = 49.5
Slide 15
Concrete Example #2
4.2.k4
Effects of Outliers
Without a zero
With a zero
Mean = 395/5 = 79
Median = 79
No mode
Range = 93 - 68 = 25
Mean = 395/6 = 65.8
Median = 76
No mode
Range = 93 - 0 = 93
IQR = 87.5 – 70.5 = 17
IQR = 86 - 36.5 = 49.5
Compare the mean, median, and mode of both scenarios.
“Which of the three measures of central tendency was
affected the most?”
Ouch!!! The mean went down about 13 points Ouch!!!
Slide 16
Step-by-Step
4.2.k4
Is it an Outlier?
Step 1: Find the inter-quartile range.
Step 2: Multiply the IQR by 1.5.
Step 3: Subtract the IQR #(1.5) from the first quartile.
Any number less than this is an outlier.
Step 4: Add the IQR #(1.5) from the third quartile.
Any number above this is an outlier.
Slide 17
Step-by-Step
4.2.k4
Things to Think About
Which measure of central tendency is ALWAYS affected the
most by an outlier? The mean.
If there is NO outlier, which measure of central tendency is
the best description of the data set? The mean.
If there is an outlier, which measure of central tendency is the
best description of the data set? Probably the median.
Slide 18