A measure of central tendency (also referred to as measures of center or central location) is a summary measure that attempts to describe a whole set of data with a single value that represents the middle or center of its distribution. The are some limitations to using the mode. In some distributions, the mode may not reflect the centre of the distribution very well. When the distribution of retirement age is ordered from lowest to highest value, it is easy to see that the centre of the distribution is 57 years, but the mode is lower, at 54 years.
8. Find the mean, median, mode, and range of the data set.
4, 7, 8, 2, 1, 2, 4, 2
Additional Example 1: Finding the Mean, Median,
Mode, and Range of Data
Mean, Median, Mode, and Range
mean:
Add the values.
4 + 7 + 8 + 2 + 1 + 2 + 4 + 2 =
Divide the sum by the number of
items.
Mean = Sum of the terms / Number
of terms
30
30 3.75
8 items
The mean is 3.75.
sum
8
=
10. Find the mean, median, mode, and range of the data set.
4, 7, 8, 2, 1, 2, 4, 2
Additional Example 1 Continued
Mean, Median, Mode, and Range
median:
Arrange the values in order.
1, 2, 2, 2, 4, 4, 7, 8
There are two middle values, so
find the mean of these two values.
The median is 3.
2 + 4 = 6
6 2 = 3
12. Find the mean, median, mode, and range of the data set.
4, 7, 8, 2, 1, 2, 4, 2
Additional Example 1 Continued
Mean, Median, Mode, and Range
mode:
The value 2 occurs three times.
1, 2, 2, 2, 4, 4, 7, 8
The mode is 2.
14. Find the mean, median, mode, and range of the data set.
4, 7, 8, 2, 1, 2, 4, 2
Additional Example 1 Continued
Mean, Median, Mode, and Range
range:
Subtract the least value
1, 2, 2, 2, 4, 4, 7, 8
The range is 7.
from the greatest value.
– 1 =
8 7
22. The line plot shows the number of miles each
of the 17 members of the cross-country team
ran in a week. Which measure of central
tendency best describes this data? Justify
your answer.
Group Activity 2: Choosing the Best Measure to
Describe a Set of Data
Mean, Median, Mode, and Range
4 6 8 10 12 14 16
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
23. The line plot shows the number of miles each
of the 17 members of the cross-country team
ran in a week. Which measure of central
tendency best describes this data? Justify
your answer.
Group Activity 2: Choosing the Best Measure to
Describe a Set of Data
Mean, Median, Mode, and Range
mean:
4 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 14 + 15 + 15 + 15 + 15 + 16 + 16
17
= 153
17
The mean is 9. The mean best describes the data
set because the data is clustered fairly evenly
about two areas.
= 9
24. The line plot shows the number of miles each
of the 17 members of the cross-country team
ran in a week. Which measure of central
tendency best describes this data? Justify
your answer.
Group Activity 2: Choosing the Best Measure to
Describe a Set of Data
Mean, Median, Mode, and Range
median:
The median is 6. The median does not best
describe the data set because many values are
not clustered around the data value 6.
4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 14, 15, 15, 15, 15,
16, 16
25. The line plot shows the number of miles each
of the 17 members of the cross-country team
ran in a week. Which measure of central
tendency best describes this data? Justify
your answer.
Group Activity 2: Choosing the Best Measure to
Describe a Set of Data
Mean, Median, Mode, and Range
mode:
The greatest number of X’s occur above the
number 4 on the line plot.
The mode is 4.
The mode focuses on one data value and does
not describe the data set.
26. The line plot shows the number of dollars each
of the 10 members of the cheerleading team
raised in a week. Which measure of central
tendency best describes this data? Justify
your answer.
Group Activity 3: Choosing the Best Measure to
Describe a Set of Data
Mean, Median, Mode, and Range
10 20 30 40 50 60 70
X
X
X
X
X
X X
X
X X
27. Group Activity 3: Choosing the Best Measure to
Describe a Set of Data
Mean, Median, Mode, and Range
mean:
15 + 15 + 15 + 15 + 20 + 20 + 40 + 60 + 60 + 70
10
= 330
10
The mean is 33. Most of the cheerleaders raised
less than $33, so the mean does not describe the
data set best.
= 33
The line plot shows the number of dollars each
of the 10 members of the cheerleading team
raised in a week. Which measure of central
tendency best describes this data? Justify
your answer.
28. Group Activity 3: Choosing the Best Measure to
Describe a Set of Data
Mean, Median, Mode, and Range
median:
The median is 20. The median best describes the
data set because it is closest to the amount most
cheerleaders raised.
15, 15, 15, 15, 20, 20, 40, 60, 60, 70
The line plot shows the number of dollars each
of the 10 members of the cheerleading team
raised in a week. Which measure of central
tendency best describes this data? Justify
your answer.
OUTLIERS
30. Group Activity 3: Choosing the Best Measure to
Describe a Set of Data
Mean, Median, Mode, and Range
mode:
The greatest number of X’s occur above the
number 15 on the line plot.
The mode is 15.
The mode focuses on one data value and does
not describe the data set.
The line plot shows the number of dollars each
of the 10 members of the cheerleading team
raised in a week. Which measure of central
tendency best describes this data? Justify
your answer.
31. Mean, Median, Mode, and Range
Measure Most Useful When
mean
median
mode
The data are spread fairly evenly
The data set has an outlier
The data involve a subject in which
many data points of one value are
important, such as election results.
33. ASSIGNMENT
1. Identify the outlier in the data set, and determine how the
outlier affects the mean, median, and mode of the data.
Then tell which measure of central tendency best describes
the data with and without the outlier. Justify your answer.
85, 91, 83, 78, 79, 64, 81, 97
The outlier is 64. Without the outlier the mean is 85, the
median is 83, and there is no mode. With the outlier the
mean is 82, the median is 82, and there is no mode.
Including the outlier decreases the mean by 3 and the
median by 1, there is no mode.
Mean, Median, Mode, and Range
35. SEAT WORK
1. Fill in the statistical summary table and refer to the given
data set below.
Mean, Median, Mode, and Range
Samples A B C D E F G H I J K L M N
Set 1 2 8 5 4 3 9 5 8 7 0 4 8 3 1
Set 2 3 4 6 4 1 2 0 5 8 7 5 9 2 7
Set 3 2 3 7 5 2 5 10 1 4 2 4 8 7 1
Set 1 Set 2 Set 3
Mean
Median
Mode
N
Measures of Central Tendency
36. SEAT WORK
1. Find the mean, median and mode for the number of days to
construct the family house.
Mean, Median, Mode, and Range
17 22 27 41 34 118
45 19 32 8 12 49
12 22 29 53 28 29
31 25 50 21 38 2
20 27 45 1 24 74
30 33 21 61 12 38
a. Calculate the measures of central tendency (mean, median & mode)
b. Identify any outliers, if there’s any.
c. How would the mean & median be affected if the outliers were removed form
the data set?
d. What measure of central tendency best describes the data set?
