Transcript DATA ANALYSIS

DATA ANALYSIS
CRCT REVIEW
Measures of Central Tendency
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
Mean
Median
Mode
Mean

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Average
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Items are added and the sum is divided by
the number of items
Mean - example
In the 12 months of 2005, it rained on 6, 8, 7, 7, 2, 2, 0,
1, 5, 6, 6, and 5 days in the town of Skeetsboro. What
is the mean number of days per month that it rained in
Skeetsboro?
6+8+7+7+2+2+0+1+5+6+6+5 = 55
55  12 = 4.6
It rained an average of 4.6 days per month in
Skeetsboro in 2005
Median
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The middle number in an ordered data set.
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Reminder: put the data in order from least to
greatest
Median - example
In the 12 months of 2005, it rained on 6, 8, 7, 7,
2, 2, 0, 1, 5, 6, 6, and 5 days in the town of
Skeetsboro. Find the median of this data.
5.5
0 1 2 2 5 5 6
5 + 6 = 11  2 = 5.5
6
6 7
7
8
Mode

The number that appears the most often in a
set of data
Mode - example
In the 12 months of 2005, it rained on 6, 8, 7, 7,
2, 2, 0, 1, 5, 6, 6, and 5 days in the town of
Skeetsboro. Find the mode of this data.
0 1 2 2 5 5 6
Mode = 6
6
6 7
7
8
Mean, Median, Mode –
Which measure of central tendency is more appropriate to
use?

In Ms. Lin’s 7th grade class, there are 21 people,
including Ms. Lin. Their ages are:
11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 37
Suppose you want to report the average age of
the people in this class. Is the mean, median, or
mode appropriate to use?
mean = 13 median is 12
mode is 12
The median and the mode are appropriate to use.
The mean is greater than the ages of 20 out of 21 people.
Mean, Median, Mode –
Which measure of central tendency is more appropriate to
use?
On eight tests this marking period, Ahmed scored
90, 82, 85, 81, 80, 90, 78, and 83. He thinks that
the mode is the most appropriate average to
describe his work. Do you agree? If you
disagree, what is the most appropriate?
mean = 83.6
median = 82.5
mode = 90
No, the mode is not the most appropriate – 6 of the 8 scores fall below
the mode.
The mean or the median is the most appropriate.
Mean, Median, Mode –
Which measure of central tendency is more appropriate to
use?
If Rasa had bowling scores of 110, 110, 125,
127, 129, and 239, is one average more
appropriate to use than the others?
mode = 110
median = 126
mean = 140
The average that is the most appropriate to use
is the median.
Measures of Variation
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Range
Quartiles
Interquartile range
Range
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The difference between the greatest and
least values in a data set
Range - example
The ten workers at a company have the following ages:
27 39 40 22 19 41 58 40 53 49
Order from least to greatest
19 22 27 39 40 40 41 49 53 58
58 – 19 = 39
The range is 39 years
Quartiles
The 3 numbers that split an ordered data set into four equal
groups

first quartile/lower quartile
–

second quartile
–

median of the lower half of the data
median of the data set
third quartile/upper quartile
–
median of the upper half of the data
Interquartile Range
Upper quartile minus lower quartile
Quartiles & Interquartile Rangeexample
Find the quartiles for the data set below.
7 9 10 11 11 12 12 13 14 16 16
LQ/Q1
IQR:
14 – 10 = 4
Q2
UQ/Q3
Types of graphs:
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pictograph:
–
a graph that shows data
using symbols or
pictures
Types of graphs (cont.):
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bar graph:
–
shows data using vertical or horizontal bars.
Types of graphs (cont.):
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histogram:
special kind of bar graph in which
the data has been grouped into
equal-sized intervals. (The bars of a
histogram touch.)
–
Types of graphs (cont.):
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line graph:
–
uses points connected by line segments to
display data. The data is collected over a period
of time. Good to use to analyze trends in data
Types of graphs (cont.):
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circle graph:
–
Each part represents a
piece of the total data.
Useful when you want to
show how a set of data
is divided among
different groups.
Types of graphs (cont.):
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stem-and-leaf plot:
–
used to organize and display data so that the
frequencies can be compared
Types of graphs (cont.):
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scatter plots:
–
points plotted show a possible relationship
between two sets of data
Types of graphs (cont.):
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box – and – whisker plot:
–
displays the highest and lowest quarters of data
as whiskers, the middle two quarters of the data
as a box, and the median.