Transcript Lesson 3-1a

3-1
6th grade math
Mean, Median, Mode and Range
Objective
• To compute the mean, median, mode, and range
of data sets
• Why? To find the measures of central tendency
as useful ways of analyzing a collection of data. To
find out more about how the data works. To find
out if the data together is statistically supportive.
California State Standards
SDP 1.1 : Compute the range, mean, median,
and mode of data sets.
SDP 1.4: Know why a specific measure of central
tendency (mean, median, mode) provides the
most useful information in a given context.
MR 1.0: To make decisions about how to approach
problems.
Vocabulary
• Measures of Central Tendency
– The mean, median, and mode in a collection
of data when the data are arranged in order
from least to greatest.
• Data Sets
– Sets of information
• Test scores, batting averages, inventory at a
clothing store, etc.
• Outliers
– A number in a data set that is very different from the
rest of the numbers
• 50, 88, 90, 90, 93, 95 = outlier is 50
• Mean
– The average of the numbers in a set of data. This type of statistic is
most mathematical. (CMT)
• 88, 90, 95 = 273 ÷ 3 = 91
• Median
– The middle number or average of the two middle numbers in a
collection data when the data are arranged in order from least to
greatest. This type of statistic helps you find the middle of a data set to
help understand above and below the average. (CMT)
• 88, 90, 95 = 90
• 88, 90, 93, 95 = 90 + 93 = 183 ÷ 2 = 91.5
• Mode
– The number(s) that occur often in a set of data. This type of statistical
data help you to know if you have too much of one value. (CMT)
• 88, 90, 90, 93, 95 = 90
• Range
– The difference between the greatest and least numbers in a
set of data. This helps you to understand the ‘range’ of
numbers.
• 88, 90, 90, 93, 95 = 95 – 88 = 7
How to Find the Mean
90, 89, 90, 100, 95, 100,
104, 100
1) Arrange data in order
from least to greatest
2) Add all numbers.
3) Divide by the amount
of numbers in the data
set. (If you round the
answer, use ~ or ≈)
89, 90, 90, 95, 100, 100,
100, 104
= 768
= 768 ÷ 8
= 96.0
How to Find the Median
90, 89, 90, 100, 95, 100, 104,
100
1) Arrange the numbers in
order from least to
greatest
2) Find the middle of the set.
3) If the set has an odd
number of values, you will
land on a middle value.
4) If the set has an even
number of values, you will
land on two middle values.
You must add those two
number as and then divide
by 2.
89, 90, 90, 95, 100, 100, 100,
104
195 ÷ 2 =
97.5
Or
≈ 98
How to Find the Mode
90, 89, 90, 100, 95, 100,
104, 100
1) Arrange the numbers in
order from least to
greatest.
2) Look for any value that is
repeated more than any
other value in the data
set.
3) There doesn’t always
need to be a mode.
89, 90, 90, 95, 100, 100,
100, 104
90 has 2 values
100 has 3 values
100 is the mode
How to Find the Range
90, 89, 90, 100, 95, 100,
104, 100
1) Arrange the numbers in
order from least to
greatest.
2) Subtract the lowest
value from the highest
3) Check your work
89, 90, 90, 95, 100,
100, 100, 104
104 – 89 = 15
Range = 15
Try It!
Find the mean, median, mode and
range for each data set.
1)
12, 14, 22, 16, 18
2)
3, 3, 3, 4, 5, 5, 5, 12
1)
Mean: 12 + 14 + 22 + 16 + 18 = 82
82 ÷ 5 = 16.4
Median: 12, 14, 16, 18, 22
= 16
Mode: none
Range: 22-12 = 10
2)
Mean: 3 + 3 + 3 + 4 + 5 + 5 + 5 + 12 = 40
40 ÷ 8 = 5
Median: 3, 3, 3, 4, 5, 5, 5, 12
4+5=9
9 ÷ 2 = 4.5
= 4.5
Mode: 3 and 5
Range: 12-3 = 9
Find the mean, median, mode and range
for each data set.
3) 1.2, 3.6, 5.4, 3, 2.4, 4.2
4) 45, 49, 40, 37, 39, 42
3)
Mean = 1.2 + 3.6 + 5.4 + 2.4 + 3 + 4.2 =
19.8 ÷ 6 =
= 3.3
Median = 1.2 + 2.4 + 3+ 3.6 + 4.2 + 5.4
3 + 3.6 = 6.6
6.6 ÷ 2 = 3.3
Mode = none
Range = 5.4 – 1.2 = 4.2
4)
Mean = 37 + 40 + 42 + 45 + 49 + 39 =
252 ÷ 6 = 42
Median = 37 + 39 + 40 + 42 + 45 + 49
40 + 42 = 82
82 ÷ 2 = 41
Mode = none
Range = 49-37 = 8
Objective Review
• To compute the mean,
median, mode, and range
of data sets.
• Why? You now can find
the measures of central
tendency as useful ways
of analyzing a collection
of data. You can also find
out more about how the
data works. You can now
know if the data together
is statistically supportive.
Independent Practice
• Complete problems 611
• 13-18
• Label MEAN, MEDIAN,
MODE, RANGE.
• Show all work!
• If time, complete Mixed
Review: 20-28
• If still more time, work
on Accelerated Math.