STATISTICS

1
STATISTICS
By Halina Kopacz
2
Learning Objectives
1) Define and calculate the range, mean, median
and mode given a set of data.
2) Categorize data as qualitative or quantitative
the relationship between correlation and
causation.
3) Construct and analyze frequency tables and
cumulative frequency tables.
4) Construct and analyze histograms and
cumulative frequency histograms.
5) Construct and analyze Box and Whisker Plots.
Click here
3
Welcome to Statistical Analysis
Statistics
Central Tendency
Frequency Tables
Histograms
Box Whiskers
Assessment
Credits
4
Statistics
Data Types
Relationships
Qualitative
Correlation
Quantitative
Causation
Example
Example
Practice
Practice
5
Qualitative Data
Deals with QUALITIES! Think of QUALITative
QUALITy
Deals with descriptions
Data can be observed but not measured
Colors, smells, textures, taste, beauty,
appearance, etc are all examples used in
qualitative data
6
Quantitative Data
Deals with QUANTITIES! Think of QUANTITative
QUANTITy
Deals with numbers
Data can be measured
Length, height, area, perimeter, volume,
weight, speed, time, temperature, cost, ages, etc
are all examples used in qualitative data
7
Lets try it together!
8
TRY IT!
Label the following as quantitative or
qualitative data.

• The tree is 10 feet tall.
• b) The horse has a brown mane.
• c) The SMART Board is shaped like a rectangle.
• d) Sarah's dog is 6 years old.
• e) It is 52o outside today.

9
To ?
10
(No Transcript)
11
Your turn now!
It is now your turn to take what you have just
learned and see if you mastered it or not.
Steps 1) Click on the link
http//regentsprep.org/Regents/math/ALGEBRA/AD1/Da
taPrac.htm
2) Complete problems 1 4. 3) When you are
finished, click answer to see the answers and the
explanation.
12
CORRELATION
Relationship between events.
13
CAUSATION
One event causes another.
Think of cause and effect.
If one action causes another (Causation), then
the two events are also correlated.
14
Examples

• Girls who watch soap operas are more
• likely to have eating disorders.

Only Correlation because watching soap operas
does not cause eating disorders

• The more a person smokes, the more likely they
  will get lung cancer.

Causation and Correlation because smoking
does cause cancer.

• The more saccharin in a rat's diet, the higher
• count of tumors in a rats .

Causation and Correlation because saccharin
does cause tumors in rats.
15
Your Turn Now!
Are the following examples of causation and
correlation or only correlation? 1)The more
miles driven, the more gasoline
needed. Causation and Correlation because the
more we drive, the more gas we need! 2)The
rooster crows and the sun rises. Correlation only
the sun will rise even with the rooster not
crowing 3)The more powerful the microwave, the
faster the food cooks. Causation and Correlation
because the stronger the microwave the more power
it produces to heat up the food. 4)The night
comes and people go to sleep. Correlation only
because some people work nights so they sleep
during the day
16
Central Tendency
Mean
Median
Mode
Range
17
MEAN

• What is it?

The average of a numerical set of data
18
MEDIAN

• What is it?

The number in the middle of the numerical set of
data
19
MODE

• What is it?

The value that occurs most frequently.c
20
RANGE

• What is it?

The difference of the greatest value and the
smallest value.
21
Computing the Mean
STEPS
1) Add up all the numbers.
2) Divide the sum by the total number of data.
If you are given the mean and need to find the
value that will lead to that mean, follow these
steps
1) Add up all the numbers.
22
Computing the Median
STEPS
1) List the numbers in numerical order.
2)Search for the number that is in the middle of
the list.
3)If there are two numbers in the middle, add
those two numbers up and divide by 2.
23
Computing the Mode
STEPS
1) Write the numbers in numerical order.
2) Look for the number that appears the most.
NOTE There may be ONE mode, NO mode at all or
MANY modes.
24
Computing the Range
STEPS
1) Write the numbers in numerical order.
2) Write the largest number and the smallest
number.
3) Subtract those two numbers.
25
EXAMPLE
Use the following data in the given table Find
the mean, median, mode range
26
Mean
Remember the mean is the average. Just add up the
numbers and divide by the total
1) Add up all the values.
251222222220215207188178
Total 1703
2) Divide by the total of data.
Total of data 8
1703
8
Answer 212.875
27
Median
1) Write the numbers in order from least to
greatest.
251,222,222,220,215,207,188,178
2) Look for the number that is in the center.
251,222,222,220,215,207,188,178
We have two numbers in the center. Therefore, we
must take the mean of those two numbers.
220 215
217.5
435
2
2
28
Mode
1) Write the numbers in order from least to
greatest.
251,222,222,220,215,207,188,178
2) Look for the number that appears the most.
222,222 appears twice therefore it is the mode.
29
Range
1) Write the numbers in order from least to
greatest.
251,222,222,220,215,207,188,178
2) Write the number that is the greatest.
The greatest number is 251.
3) Write the number that is the smallest.
The smallest number is 178.
4) Subtract the two numbers.
251 - 178
78
30
Your Turn Now!
It is now your turn to take what you have just
learned and see if you mastered it or not.
Steps 1) Click on the link
http//regentsprep.org/Regents/math/ALGEBRA/AD2/Pm
easure.htm
2) Complete problems 1 6. 3) When you are
finished, click answer to see the answers and the
explanation.
31
Frequency Tables
Cumulative Frequency Tables
Frequency
32
Frequency Tables
Example
What is it?
A type of data displayed in a table of tally
marks used to record and display how often events
occur.
33
Constructing
Steps to Constructing a Frequency Table
1) Make a table with the following headings
Interval, Tally, Frequency
2) Choose an interval that is of EQUAL length and
covers all data.
3) Make a tally mark in the tally column of each
number that lies in that data range.
4) Add up all the tally marks for the interval
and place that number in the frequency
column.
34
Example
The data below are scores on a mathematics test
for 20 students. Create a frequency distribution
table. 90, 75, 84, 63, 100, 58, 70, 78, 61, 72,
55, 91, 67, 79, 52, 86, 90, 77, 63, 74
Complete Steps One And Two!
Example Page 2
35
Example
The data below are scores on a mathematics test
for 20 students. Create a frequency distribution
table. 90, 75, 84, 63, 100, 58, 70, 78, 61, 72,
55, 91, 67, 79, 52, 86, 90, 77, 63, 74
Complete Step Three!
Example Page 3
36
Example
The data below are scores on a mathematics test
for 20 students. Create a frequency distribution
table. 90, 75, 84, 63, 100, 58, 70, 78, 61, 72,
55, 91, 67, 79, 52, 86, 90, 77, 63, 74
Complete Step Four and You are Done! Congrats!
37
Practice
38
Cumulative Frequency Tables
Cumulative Frequency Table Example
What is it?
A type of data displayed in a table in which the
frequencies are accumulated for each item. We
continue to add up the previous tally to our
new tally.
39
Constructing
Steps to Constructing a Cumulative Frequency
Table
1) Make a table with the following headings
Interval, Tally, Frequency, Cumulative Frequency
2) Choose an interval that is of EQUAL length and
covers all data.
3) Make a tally mark in the tally column of each
number that lies in that data range.
4) Add up all the tally marks for the interval
and place that number in the frequency
column.
5) Add number to previous frequency
40
Example
Use the frequency table we already created. The
data below are scores on a mathematics test for
20 students. Create a frequency distribution
table. 90, 75, 84, 63, 100, 58, 70, 78, 61, 72,
55, 91, 67, 79, 52, 86, 90, 77, 63, 74
Example Page 2
41
Example
Use the frequency table we already created. The
data below are scores on a mathematics test for
20 students. Create a frequency distribution
table. 90, 75, 84, 63, 100, 58, 70, 78, 61, 72,
55, 91, 67, 79, 52, 86, 90, 77, 63, 74
42
Your Turn!
43
Histograms
Histograms
Cumulative Frequency Tables
Frequency
44
What is it?

• Frequency Histogram is a bar graph that displays
  data from a Frequency Table.

45
Constructing
46
Example
Given the following frequency table, construct a
frequency histogram. Click here to go to the graph
Page 2 of the example
47
Example Page 2
FREQUENCY TABLE
9
8
7
6
5
FREQUENCY
4
3
2
1
0
91-100
41-50
51-60
61-70
71-80
81-90
INTERVAL
48
Your Turn Now!
It is now your turn to take what you have just
learned and see if you mastered it or not.
Steps 1) Click on the link
http//regentsprep.org/Regents/math/ALGEBRA/AD3/Pr
acData.htm
2) Complete problems 1b (only the frequency) and
5a. Note you will practice the other skills
you learned on these questions as well!! 3)
When you are finished, click answer to see the
answers and the explanation.
49
What is it?
Cumulative Frequency Histogram is a histogram
using a cumulative frequency table.

• Cumulative is a running tally of the frequencies.

Keep adding the tallies up until the final
interval has the total amount data given.
50
Constructing
There are five steps to constructing a Cumulative
Frequency Histogram.
Steps
1) Construct an x and y axis
Example of your histogram set up!
2) Write the cumulative intervals on the bottom
of your x-axis.
3) Write the frequencies on your y-axis
4) Draw a bar for each interval. DO NOT LEAVE A
SPACE BETWEEN EACH INTERVAL.
5) Add a title to your cumulative histogram!
51
Example
Given the following cumulative frequency table,
construct a cumulative frequency histogram. Click
here to go to the graph
52
Your Turn Now!
It is now your turn to take what you have just
learned and see if you mastered it or not.
Steps 1) Click on the link
http//regentsprep.org/Regents/math/ALGEBRA/AD3/Pr
acData.htm
2) Complete problems 1b and 5b. Note you will
practice the other skills you learned on
these questions as well!! 3) When you are
finished, click answer to see the answers and the
explanation.
53
Box Whisker Plots
Quartiles
Constructing
Q1
Q2
Q3
54
What is a Box and Whisker Plot?
A display of data that divides a set of data into
five parts called the statistical summaries.
Statistical Summary is comprised of a Minimum,
Maximum, 2nd Quartile, 1st Quartile, and 3rd
Quartile.
55
Quartile 1
What is it?
The median of the lower half of data.
56
Quartile 2
What is it?
The median of the data.
Splits the data into two equal parts.
57
Quartile 3
What is it?
The median of the upper half of the data.
58
Computing Quartile 1
59
Computing Quartile 2
60
Computing Quartile 3
61
Example
Click on Q1, Q2, or Q3 to go to the answer!
Lets Determine the Three Quartiles
Given the following data, determine Q1, Q2, and
Q3.
2,10,12,16,17,17,18,18,20,22
Find Q2 first!
62
Quartile 1
2,10,12,16,17,17,18,18,20,22
63
Quartile 2
2,10,12,16,17,17,18,18,20,22
Since we have two medians, we must find the mean!
64
Quartile 3
2,10,12,16,17,17,18,18,20,22
Median of the upper half
Median
65
Your Turn Now!
It is now your turn to take what you have just
learned and see if you mastered it or not.
Steps 1) Click on the link
http//regentsprep.org/Regents/math/ALGEBRA/AD3/Pr
acData.htm
2) Complete problems 3 and 6. Note you will
practice the other skills you learned on
these questions as well!! 3) When you are
finished, click answer to see the answers and the
explanation.
66
Constructing Box Whisker Plots
Video
Written Steps
67
Steps to Making a Box and Whisker Plot

• Put the data in order.
• Find the median
• Find the quartiles (medians of the upper and
  lower halves).
• Plot the median, and the quartiles below a number
  line.
• Plot the maximum and minimum values below the
  number line.
• Draw a box from the lower quartile to the upper
  quartile.
• Draw a vertical line through the median.
• Draw line segments (whiskers) from the box to the
  maximum value and from the box to the minimum
  value.

68
Example 1

• The lengths of songs (in seconds) on a CD are
  listed below. Make a box and whisker plot of the
  song lengths.
• 173, 206, 179, 257, 198, 251, 239, 246, 295, 181,
  261

1. Put the data in order. 173,179, 181, 198,
206, 239, 246, 251, 257, 261, 295 2. Find the
median 173,179, 181, 198, 206, 239, 246, 251,
257, 261, 295 3. Find the quartiles (medians of
the upper and lower halves). 173,179, 181, 198,
206, 239, 246, 251, 257, 261, 295
Page 2 of the example
69
Example 1 continued

• 4. Plot the median, and the quartiles below a
  number line.
• 5. Plot the maximum and minimum values below the
  number line.
• 6. Draw a box from the lower quartile to the
  upper quartile.
• 7. Draw a vertical line through the median.
• 8. Draw line segments (whiskers) from the box to
  the maximum value and from the box to the minimum
  value.

255
270
285
300
165
195
180
240
225
210
70
Try It!

• Make a box-and whisker plot of the ages of eight
  family members.
• 60, 15, 25, 20, 55, 70, 40, 30

15, 20, 25, 30, 40, 55, 60, 70
10
20
30
40
50
60
70
3040/235
2025/222.5
5560/257.5
71
Lets Try It Again!
72
(No Transcript)
73
(No Transcript)
74
Assessment
http//www.regentsprep.org/Regents/math/ALGEBRA/Mu
ltipleChoiceReview/WorkingData.htm
75
Credits and Bibliography

• http//teachers.henrico.k12.va.us/math/HCPSAlgebra
  1/module10review.html