Chapter 14
Statistics and Data Analysis
Data Analysis Chart Types

Line Plot

Uses a symbol to show frequency
Data Analysis Chart Types

Bar Graph

Uses bars to indicate frequency
Data Analysis Chart Types

Back-to-Back bar graph

A special bar graph that shows the
comparisons of two sets of related data
Data Analysis Chart Types

Three Dimensional Bar Graph

Used when showing three aspects of a set
of data at the same time
Data Analysis Chart Types

Stem and Leaf Plot
Used to organize a large number of data
 Stem

Column on the left
 usually digits in the greatest common place
value of data


Leaf
Column on the right
 one digit numbers, which are in the next greatest
place value after the stem

Data Analysis Chart Types

Create a stem and leaf plot for the data below.
 The
following are the grades scored on
a quiz with 50 possible points
 42,
49, 36, 32, 10,19,38,40,41,
50,40,49,30,20,48,47,40,41,32,
37,25,41,43,37,39
 What

is the first thing you need to do?
Write in numerical order
Data Analysis Chart Types

Histogram
Most common way of displaying frequency
distributions
 Type of bar graph in which the width of each
bar represents a class interval and the
height of the bar represents the frequency in
that interval.

Data Analysis Chart Types
Data Analysis Chart Activity
Get in groups of 3 or 4
 You will be making a data analysis chart
to display and explain to the class


You can look at things like:
Brothers and Sisters
 How many days you workout, go to the beach,
read a book, play a sport, etc each week
 States visited

 Be
creative!
Measures of Central Tendency

Measures of Central Tendency
Measures of averages
 Mean
 Median
 Mode


Arithmetic Mean

X, adding the values of the set of data and
dividing by the number of values of the data
Measures of Central Tendency
General Formula
 Find the mean of (36.8, 29.5, 29.1, 33.3,
30.0, 20.7, 39.5)


About 31.3
Measures of Central Tendency

Median
 The middle value
 If there are two middle values, then it is the
mean of the two middle values
 What is the median of (5,6,8,11,14)?
8
 What is the median of (3,4,6,7,8,10)?
 (6+7)/2=6.5
 Doesn’t have to be part of original data
set
Measures of Central Tendency

Mode
Most frequent value
 Some sets may have multiple modes and
others can have none
 Data with two modes are called “bimodal”
 Mode, unlike mean and median, has to be
part of the data set

Example

What is the mean,
median and mode of
the data?



Mean 45.2
Median46.5
Mode46
Year
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
# of HR
11
29
54
59
41
46
47
60
54
46
49
46
Measures of Central Tendency

Recall this example from Lesson 1:
 The following are the grades scored on a quiz
with 50 possible points
 42, 49, 36, 32, 10,19,38,40,41,50,40,49,
30,20,48,47,40,41,32, 37,25,41,43,37,39
 Now,
use your steam and leaf plot to
help find the mean, median, and mode
for the data
Mean 37.04
 Median 40
 Mode40,41

Frequency Distribution Activity

Get into partners and complete the
following with your specific data set:
 Find
the mean, median, and Mode
Box and Whisker Plot

Measures of Variability


Range of a data set
QuartilesQ1, Q2 , Q3
Which Quartile is the median of the data?
 Q2
 Interquartile Range
 (Q3-Q1)
 Semi-Interquartile Range
 (Q3-Q1)/2

Box and Whisker Plot

Find the interquartile range of the
following test scores
 82,
78, 94, 68, 74, 88, 64, 42, 72,
82, 79, 99
 Write in order first.
 What is the mean, median, and
mode?
Box and Whisker Plot
 82,
78, 94, 68, 74, 88, 64, 42,
72, 82, 79, 99

Mean •What are Q1, Q2 , Q3?


Median


77
78
Mode

82
•Q1=69 •Interquartile Range
•Q2=78
•Q3=86
•17
•Semi-interquartile Range
•8.5
Box and Whisker Plot

Box-and-whisker plots
 Used to summarize data and illustrates the variability
of the data
 Displays median, quartiles, interquartile range, and
extreme values
 Box consists of Quartiles 1 and 3
 Whiskers stop at the extreme values of the set
 Outliers
 Values that are more than 1.5 times the
interquartile range beyond the upper or lower
quartiles
Box and Whisker Plot

Draw a box-and-whisker plot for the test
scores in first example.
 82,
78, 94, 68, 74, 88, 64, 42, 72,
82, 79, 99
Measures of Variability in Data Set

Mean Deviation
The average absolute value distance each
piece of data is from the mean
 Formula
n

1
 MD=
|X i  X |

n i 1

What is the mean deviation of our example?
Mean Deviation Example

Recall previous box and whisker
example:
 82,
78, 94, 68, 74, 88, 64, 42, 72,
82, 79, 99

Find Mean Deviation
Frequency Distribution Activity

Get into partners and complete the
following with your specific data set:
 Make
a Box and Whisker Plot with
all necessary information for your
specific data set.
 Find the mean deviation for your
data set.
Measures of Variability in Data Set

Standard Deviation
Measures of the average amount each
piece of data deviates from the mean
 Formula

Measures of Variability in Data Set

Variance
Describes the spread of the data
 Mean of the squares of the deviations from
the average

 =δ2

Therefore standard deviation is the positive
square root of the variance
Measures of Variability in Data Set
 What
is the variance and standard
deviation for our test score
example?
 Variance
 Standard Deviation
Frequency Distribution Activity

Get into partners and complete the
following with your specific data set:
 Variance
and Standard deviation
for your data set.
 Reflect on what these measures
tell you about the data.
Measures of Variability in
Frequency Distribution

Standard Deviation of the Data in a
Frequency Distribution
n
X 
(X
i 1
 X ) * fi
2
i
n
f
i 1
i
Measures of Variability in
Frequency Distribution

Variance of the Data in a Frequency
Distribution
 =δ2
Measures of Variability in
Frequency Distribution
 Make
a frequency distribution for the
test score example from the box and
whisker plot lesson below.
 82, 78, 94, 68, 74, 88, 64, 42, 72,
82, 79, 99

What is the variance, standard deviation,
and mean deviation from this frequency
distribution?
The Normal Distribution
A frequency distribution that occurs
when there is a large number of values
in a set of data
 Looks like a symmetric bell-shaped
curve called a normal curve
 Shape of the curve comes from a large
number of frequencies falling in the
middle of the distribution; small percent
fall at the extreme values

The Normal Distribution
About 95.2% of the data
are within 2 standard
deviations from the mean
About 99.6% of the data are within 3 standard
deviations from the mean
About 68% of the data
are within 1 standard
deviation from the mean.
The Normal Distribution
Represents those values
that fall between two and
three standard deviations
below the mean
Mean Value
Represents those values
that fall between one and
two standard deviations
above the mean
The Normal Distribution

The average healing time of a certain type of
incision is 240 hours with a standard deviation
of 20 hours. What does the normal curve look
like?


First put in the mean; Then figure out each interval
How many patients healed in the 220-260 hour
interval if there were a total of 2000 patients?


68.3%*(2000)=1366
How many patients healed in the 180-300 hour
interval if there were a total of 2000 patients?

1994
Review 14.3

Find the variance and standard deviation
for the data set below:


12, 22, 25, 27, 15, 18
Put the following data into a frequency
distribution and then find the variance and
standard deviation:

11, 16, 18, 25, 29, 22, 24, 5, 9, 2