Download SECTION 6.6 Stem-and-Leaf Plots and Mean, Median, and Mode

SECTION 6.6
Stem-and-Leaf Plots and
Mean, Median, and Mode
WHAT’S IMPORTANT:
-- Be able to make and use a stemand-leaf plot to put data in order.
-- Be able to find the mean, median,
and mode of data.
Section 6.6: “Stem-and-Leaf Plots
and Mean, Median, and Mode”
Stem-and-Leaf Plot: An arrangement of digits
that is used to display and order numerical data.
The stems are usually all digits except the last
digit.
The leaves are usually the last digit.
For example, the number in the plot below is 45.
Stem
4
Leaf
5
Section 6.6: “Stem-and-Leaf Plots
and Mean, Median, and Mode”
Example: The data shows the ages of 24
patients who were treated in one day at a health
clinic. Make a stem-and-leaf plot of the data.
25 12 30 20 15 21 16 13
18 27 43 23 19 22 20 67
53 19 25 66 35 11 20 37
Stem
Leaf
1 1 2 3 5 6 8 9 9
2 0 0 0 1 2 3 5 5 7
3 0 5 7
4 3
5 3
Key: 4|3 = 43
6 6 7
Section 6.6: “Stem-and-Leaf Plots
and Mean, Median, and Mode”
Example: The data shows the ages of 10
runners on the track team. Make a stem-andleaf plot of the data.
15 25 12 36 48
10 12 30 12 17
Stem
1
2
3
4
Leaf
0 2 2 2 5 7
5
0 6
8
Key: 4|8 = 48
Section 6.6: “Stem-and-Leaf Plots
and Mean, Median, and Mode”
Mean: Another word for “average”. Found by
adding the numbers up and dividing the sum by
the amount of numbers present.
Median: The middle number when the numbers
are written in order. If there is no “middle
number”, then you add the two middle numbers
and divide by 2.
Mode: The number that occurs most frequently.
A set of data can have more than one mode….or
no mode.
Section 6.6: “Stem-and-Leaf Plots
and Mean, Median, and Mode”
Example: Find the mean, median, and mode
of the data given.
4, 2, 10, 6, 10, 7, 10
Mean = 49/7 = 7
2, 4, 6, 7, 10, 10, 10
Median = 7
Mode = 10
Section 6.6: “Stem-and-Leaf Plots
and Mean, Median, and Mode”
Example: Find the mean, median, and mode
of the data given.
8, 5, 6, 6, 5, 6
Mean = 36/6 = 6
5, 5, 6, 6, 6, 8
Median = 6
Mode = 6
Section 6.6: “Stem-and-Leaf Plots
and Mean, Median, and Mode”
Make a stem-and-leaf plot of the data.
11 30 24 41 22
18 14 32 11 62
Stem
1
2
3
4
5
6
Leaf
1 1 4 8
2 4
0 2
1
Key: 4|1 = 41
2
Section 6.6: “Stem-and-Leaf Plots
and Mean, Median, and Mode”
Example: Find the mean, median, and mode
of the data given.
Mean = 440/10 = 44
Median = (44 + 50)/2 = 94/2 = 47
Mode = 51
Leaf
Stem
3 0 3 4
4 2 4
5 0 1 1 1 4
Key: 3|0 = 30
Section 6.6: “Stem-and-Leaf Plots
and Mean, Median, and Mode”
Example: Find the mean, median, and mode
of the data given.
5, 3, 10, 13, 8, 18, 5,
17, 2, 7, 9, 10, 4, 1
Mean = 112/14 = 8
1, 2, 3, 4, 5, 5, 7, 8, 9, 10, 10, 13, 17, 18
Median = 7.5
Mode = 5 and 10
Section 6.6: “Stem-and-Leaf Plots
and Mean, Median, and Mode”
Example: Find the mean, median, and mode
of the data given.
Mean = 657/24 = 27.375
Median = (21 + 22)/2 = 43/2 = 21.5
Mode = 20
Stem
1
2
3
4
5
6
Leaf
1 2 3 5 6 8 9 9
0 0 0 1 2 3 5 5 7
0 5 7
3
3
Key: 5|3 = 53
6 7
► 1.
Solve |𝟐𝒙 − 𝟓| = 𝟏𝟏
𝟐𝒙 − 𝟓= 11
or
𝟐𝒙 − 𝟓= −𝟏𝟏
+5 +5
+5 + 5
𝟐𝒙 = 16
𝟐𝒙 = −𝟔
𝟐
𝟐
𝟐
𝟐
𝒙= 𝟖
or
𝒙 = −𝟑
𝒙 = −𝟑, 𝟖
► 2.
Solve |𝟒𝒙 − 𝟐| = 𝟐𝟐
𝟒𝒙 − 𝟐 = 𝟐𝟐
or
+𝟐 + 𝟐
𝟒𝒙 = 𝟐𝟒
𝟒
𝟒
𝒙=𝟔
or
𝟒𝒙 − 𝟐 = −𝟐𝟐
+𝟐 + 𝟐
𝟒𝒙 = −𝟐𝟎
𝟒
𝟒
𝒙 = −𝟓
1.
Solve
𝟑𝒙 − 𝟗 + 𝟕 = 𝟔𝟕
−𝟕 − 𝟕
𝟑𝒙 − 𝟗 = 𝟔𝟎
𝟑𝒙 − 𝟗 = 𝟔𝟎
or
𝟑𝒙 − 𝟗 = −𝟔𝟎
+𝟗 + 𝟗
+𝟗 + 𝟗
𝟑𝒙 = 𝟔𝟗
𝟑𝒙 = −𝟓𝟏
𝒙 = 𝟐𝟑
or
𝒙 = −𝟏𝟕
► 2.
Solve 𝟐𝒙 + 𝟑 + 𝟒 = 𝟐𝟕
−𝟒 − 𝟒
𝟐𝒙 + 𝟑 = 𝟐𝟑
𝟐𝒙 + 𝟑 = 𝟐𝟑
or
𝟐𝒙 + 𝟑 = −𝟐𝟑
−𝟑 − 𝟑
−𝟑
−𝟑
𝟐𝒙 = 𝟐𝟎
𝟐𝒙 = −𝟐𝟔
𝒙 = 𝟏𝟎
or
𝒙 = −𝟏𝟑
1. Write an equation of the line that passes
through the points (𝟎, −𝟓) and (𝟑, 𝟒).
𝟒−(−𝟓)
• Slope (𝑚)=
𝟑−𝟎
𝒚 = 𝟑𝒙 + 𝒃
−𝟓 = 𝟐 𝟎 + 𝐛
−𝟓 = 𝟎 + 𝒃
−𝟓 = 𝒃
=
𝟗
𝟑
𝒐𝒓 𝟑
𝒚 = 𝟑𝒙 − 𝟓
2. Write an equation of the line that passes
through the points (𝟐, 𝟎) and (−𝟐, 𝟔).
𝟔−𝟎
𝟔
𝟑
Slope (𝑚) =
=
𝒐𝒓 −
𝟑
𝟎 = − (𝟐) + 𝒃
𝟐
𝟎 = −𝟑 + 𝐛
+𝟑 + 𝟑
𝟑=𝒃
−𝟐−𝟐
−𝟒
𝟐
𝟑
𝒚=− 𝒙+𝟑
𝟐
Solving a Compound Inequality with Or
Solve 3x +𝟐 < 𝟏𝟕 or 2x – 8 ≥ 4. Graph the solution.
SOLUTION
A solution of this inequality is a solution of either of its simple parts.
You can solve each part separately.
3𝒙 + 𝟐 < 𝟏𝟕
−𝟐 −2
3x < 𝟏𝟓
3
3
x<𝟓
or
or
or
𝟐𝒙 − 𝟖 ≥ 𝟒
+𝟖 + 𝟖
2x ≥ 12
2
2
x≥6
0 1 2 3 4 5 6 7 8
Solving a Compound Inequality with And
Solve −𝟏𝟑 ≤ -2x + 3 < −7. Graph the solution.
SOLUTION
Isolate the variable x between the two inequality symbols.
−𝟏𝟑 ≤ −2x + 3 < −7
−𝟑
−𝟑 −𝟑
−𝟏𝟔 ≤ −𝟐x < -10
−𝟐 − 𝟐
−𝟐
Write original inequality.
Subtract 3 from each expression.
Divide each expression by -2.
8 ≥ x >5
𝟓<𝒙≤𝟖
5
6
7
8
9