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Stem-and-Leaf Plots page 653.
EXAMPLE 1
Making a Stem-and-Leaf Plot
To organize the minutes online in the table above, you
can make a stem-and-leaf plot. The numbers range
from 15 to 70. So, the least stem is 1 and the greatest
stem is 7.
EXAMPLE 1
Making a Stem-and-Leaf Plot
To organize the minutes online in the table above, you
can make a stem-and-leaf plot. The numbers range
from 15 to 70. So, the least stem is 1 and the greatest
stem is 7.
STEP 1
Order stems from least to greatest.
1
2
3
4
5
6
7
EXAMPLE 1
Making a Stem-and-Leaf Plot
STEP 2
Write the leaves next to their stems.
1
2
3
4
5
6
7
959
27398
51175
2104
430
0
This stands for
53.
EXAMPLE 1
Making a Stem-and-Leaf Plot
STEP 3
Order the leaves from least to greatest.
1
2
3
4
5
6
7
599
23789
11557
0124
034
0
Key: 5 3 = 53
Be sure to include a key.
GUIDED PRACTICE
for Example 1
1. Make a stem-and-leaf plot of the data 31, 14, 22, 51, 33,
16, 21, 24, 22, 15, 30, 28, and 39.
EXAMPLE 2
Interpreting Stem-and-Leaf Plots
Diners
The stem-and-leaf plot shows the ages of people at a
diner.
0 4679
1 01122249
2 258
3 014
Key: 3 1= 31
EXAMPLE 2
Interpreting Stem-and-Leaf Plots
Diners
The stem-and-leaf plot shows the ages of people at a
diner.
0 4679
a. What is the range of the ages? 1 0 1 1 2 2 2 4 9
2 258
3 014
Key: 3 1= 31
EXAMPLE 2
Interpreting Stem-and-Leaf Plots
Diners
The stem-and-leaf plot shows the ages of people at a
diner.
0 4679
a. What is the range of the ages? 1 0 1 1 2 2 2 4 9
2 258
3 014
Key: 3 1= 31
SOLUTION
a. The youngest person at the diner is 4
years old, because the least data
value is 0 | 4. The oldest is 34 years
old, because the greatest data value
is 3 | 4. The range is 30 years, because
34 – 4 = 30.
EXAMPLE 2
Interpreting Stem-and-Leaf Plots
b. Describe the age group with
the most people.
SOLUTION
0
1
2
3
4679
01122249
258
014
Key: 3 1= 31
The stem of 1 has more leaves than any other, so
the age group with the most people is 10 – 19 years.
Mean, Median, Mode, & Range pg. 93
Central Tendencies
Mean (
Add all of the numbers
Divide the answer by how
many numbers you added.
5, 6, 8, 5, 7, 11 = 42
42 ÷ 6 = 7
MOde
)
Median
When a set of data is in
Numerical order the median
Is the number in the middle
5, 5, 6, 7, 8, 11 = 6.5
6 + 7 = 13
13 ÷ 2 = 6.5
The number(s) that occur
MOst often:
Or
In an odd set of numbers
5, 6, 8, 5, 7, 11
5, 5, 6, 7, 8 = 6
R
a The difference
Between
largest
n TheAnd
Smallest
g Numbers.
e 11 – 5 = 6
Essential Question:
Collect data
Mean
sum of all data values
divided by the
number of values,
sometimes called the
AVERAGE, affected
by all values
Median:
middle value once the
numbers are placed in
order (If two numbers
are in the middle, add
the numbers and divide
by two)
Mode:
value(s) that
occurs the
MOST often.
There can be
more than one
mode
Range:
The difference
between the
largest number
and the smallest
number.
Mean
• 4, 5, 6, 4, 7, 4,
• Step 1: add all values together
• Step 2: Divide the sum by the number of
values.
• The quotient is the mean.
• Return
Finding Mean:
Mean
Return
Median
• 4, 5, 6, 4, 7, 4,
• First put the numbers in numerical order.
• Find the number in the middle. Take one off
of each end until you only have one number
left.
• If you have two numbers left find their
mean and it will be the median.
• Return
Mode
• 4, 5, 6, 4, 7, 4,
• The number(s) that occur the most.
• If all numbers occur only one time there is
no mode.
• Return
Range
• 4, 5, 6, 4, 7, 4,
• Find the Largest number and the smallest
number.
• Subtract them.
• The difference is the range.
• Return
Teachertube: Brainpop
The Measures of Central Tendency & Range
Essential
EssentialQuestion:
Question:
Collect Data
Mean
sum of all data
values divided
by the number
of values,
sometimes
called the
AVERAGE,
affected by all
values
Median:
middle value
once the
numbers are
placed in order
(If two numbers
are in the
middle, add the
numbers and
divide by two)
Mode:
value(s) that
occurs the
MOST often.
There can be
more than
one mode
Range:
The difference
between the
largest number
and the
smallest
number.
EXAMPLE 3
Finding the Mean, Median, and Mode
Use the stem-and-leaf plot shown below.
5 77
a. Find the mean.
b. Find the median.
6 127
c. Find the mode.
7 0 4 Key: 5 7 = 5.7
SOLUTION
Make an ordered list of the 7 values in the stem-andleaf plot.
5.7, 5.7, 6.1, 6.2, 6.7, 7.0, 7.4
a. Mean = 5.7 + 5.7 + 6.1 + 6.2 + 6.7 + 7.0 + 7.4 = 44.8 = 6.4
7
7
EXAMPLE 3
Finding the Mean, Median, and Mode
Use the stem-and-leaf plot shown below.
5 77
a. Find the mean.
b. Find the median.
6 127
c. Find the mode.
7 0 4 Key: 5 7 = 5.7
SOLUTION
Make an ordered list of the 7 values in the stem-andleaf plot.
5.7, 5.7, 6.1, 6.2, 6.7, 7.0, 7.4
b. Median = 6.2, because the middle value is 6.2.
EXAMPLE 3
Finding the Mean, Median, and Mode
Use the stem-and-leaf plot shown below.
5 77
a. Find the mean.
b. Find the median.
6 127
c. Find the mode.
7 0 4 Key: 5 7 = 5.7
SOLUTION
Make an ordered list of the 7 values in the stem-andleaf plot.
5.7, 5.7, 6.1, 6.2, 6.7, 7.0, 7.4
c. Mode = 5.7, because it is the only value that occurs
more than once.
GUIDED PRACTICE
for Examples 2 and 3
2. Use the stem-and-leaf plot in Example 2. How
many people at the diner are over 20 years old?
What are their ages?
0 4679
1 01122249
ANSWER
2 258
3 014
6; 22, 25, 28, 30, 31, and 34
Key: 3 1= 31
GUIDED PRACTICE
for Examples 2 and 3
Find the mean, median, and mode(s) of the data.
GUIDED PRACTICE
for Examples 2 and 3
Find the mean, median, and mode(s) of the data.
3. 3
4
5
6
179
2236
04777
258
Key: 3 1 = 31
GUIDED PRACTICE
for Examples 2 and 3
Find the mean, median, and mode(s) of the data.
3. 3
4
5
6
179
2236
04777
258
Key: 3 1 = 31
ANSWER
50, 50, 57
GUIDED PRACTICE
for Examples 2 and 3
5. 1 2 3 5 9
2 36789
3
4 11246
Key: 1 2 = 12
GUIDED PRACTICE
for Examples 2 and 3
5. 1 2 3 5 9
2 36789
3
4 11246
Key: 1 2 = 12
ANSWER
29, 27.5, 41
Workbook pg. 179-180
Workbook pg. 179-180
Workbook pg.179-180