Mean, Median, Mode, Range and Stem and Whisker Plots

1. Mean, Median, Mode and Range
Introduction to Statistics
Grade 7 Pre-Algebra
Ms. Moran

2. Vocabulary
• Mean
 The sum of the data in a set divided by the
number of items of data. Aka the average.
• Median
 The middle number of a group of data that has
been arranged in numerical order.
• Mode
 The number that occurs most often.
• Range
 The difference between the greatest and the
least numbers.
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3. Mean
•
Does NOT refer to Ms. Van Beek!
•
How to find the mean of a group of data:
 Take all the numbers and add them together.
 Count how many numbers you added.
 Divide the sum of the numbers by that number.
•
Example 1:
 The weights of 9 students, measured in pounds, are
recorded below. Find the mean weight.
• 135, 120, 116, 119, 121, 125, 135, 131, 123
•
Example 2:
 The mean price of 5 items is $7.00. The prices of the
first four items are $6.50, $8.00, $5.50 and $6.00.
How much does the fifth item cost?
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4. Median
• How to find the median of a group of data:
 Place all of the numbers in order in increasing value.
 The middle number is the median.
 If there are two middle numbers, then the median is the
average of the two middle numbers.
•
Example 1:
 The weights of 9 students, measured in pounds, are recorded
below. Find the median of the weights.
• 135, 120, 116, 119, 121, 125, 135, 131, 123
•
Example 2:
 The grade point averages of 10 students are listed below. Find
the median grade point average.
• 3.15, 3.62, 2.54, 2.81, 3.97, 1.85, 1.93, 2.63, 2.50, 2.80
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5. Mode
• How to find the mode of a group of data:
 Tally the number of times each of the numbers appears in
the group of numbers.
 The mode is the number that is written the most often.
•
Example 1:
 In a crash test, 11 cars were tested to determine what impact speed
was required to obtain minimal bumper damage. Find the mode of the
speeds given in miles per hour below.
• 24, 15, 18, 20, 18, 22, 24, 26, 18, 26, 24
•
Example 2:
 A marathon race was completed by 5 participants. What is the mode of
these times given in hours?
• 2.7 hr, 8.3 hr, 3.5 hr, 5.1 hr, 4.9 hr
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6. Range
•
How to find the range of a group of data:
 Find the largest number of the group.
 Find the smallest number of the group.
 The range is the largest number minus the lowest
number in a set of data.
•
Example 1:
 The weights of 9 students, measured in pounds, are recorded
below. Find the range of the weights.
• 135, 120, 116, 119, 121, 125, 135, 131, 123
•
Example 2:
 The range of a set of numbers is 1,362. The largest number is
2,172. What is the smallest number?
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7. Stem-and-Leaf Plots
Box-and-Whisker Plots
You can do it!

8. Stem-and-Leaf Plots
•
Data can be displayed in many ways. One method of
displaying a set of data is with a stem-and-leaf plot.
A stem-and-leaf plot is a display that organizes data to
show its shape and distribution.
•
In a stem-and-leaf plot each data value is split into a
"stem" and a "leaf". The "leaf" is usually the last digit of
the number and the other digits to the left of the "leaf"
form the "stem".
•
The number 123 would be split as:
 Stem
12
 Leaf
3
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9. Constructing a Stem-and-Leaf Plot
•
The data: Math test scores out of 50 points:
 35, 36, 38, 40, 42, 42, 44, 45, 45, 47, 48, 49, 50, 50, 50.
Writing the data in numerical
order may help to organize the
data, but is NOT a required step.
Ordering can be done later.
35, 36, 38, 40, 42, 42, 44, 45,
45, 47, 48, 49, 50, 50, 50
The number 38 would be represented as:
Separate each number into a
stem and a leaf. Since these are
Stem Leaf
two digit numbers, the tens digit
is the stem and the units digit is
3
8
the leaf.
Title the plot graph. Group the
numbers with the same stems.
List the stems in numerical
order. (If your leaf values are
not in increasing order, order
them now.)
Prepare an appropriate legend
(key) for the graph.
Math Test Scores
(out of 50 pts)
Stem
Leaf
3
5 6 8
4
0 2 2 4 5 5 7 8 9
5
0 0 0
Legend: 3 | 6 means 36
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10. Box-and-Whisker Plots
•
Data can be displayed in many ways. One method of
displaying a set of data is with a box-and-whisker plot.
Box-and-whisker plots are helpful in interpreting the distribution
of data.
 We know that the median of a set of data separates the
data into two equal parts. Data can be further separated
into quartiles.
• The first quartile is the median of the lower part of the data.
• The second quartile is another name for the median of the
entire set of data.
• The third quartile is the median of the upper part of the data.
•
Quartiles separate the original set of data into four equal parts.
Each of these parts contains one-fourth of the data.
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11. Constructing a Box-and-Whisker
Plot
• The data: Math test scores 80, 75, 90, 95, 65, 65, 80, 85, 70, 100
Write the data in numerical
order and find the first quartile,
the median, the third quartile,
the smallest value and the
largest value.
median = 80
first quartile = 70
third quartile = 90
smallest value = 65
largest value = 100
Place a circle beneath each of
these values on a number line.
Draw a box with ends through
the points for the first and third
quartiles. Then draw a vertical
line through the box at the
median point. Now, draw the
whiskers (or lines) from each
end of the box to the smallest
and largest values.
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