1. Statistics and Data Analysis
Chapter 14
Statistics and Data Analysis

2. Data Analysis Chart Types
Line Plot
Uses a symbol to show frequency

3. Data Analysis Chart Types
Bar Graph
Uses bars to indicate frequency

4. Data Analysis Chart Types
Back-to-Back bar graph
A special bar graph that shows the comparisons of two sets of related data

5. Data Analysis Chart Types
Three Dimensional Bar Graph
Used when showing three aspects of a set of data at the same time

6. 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

7. 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

8. 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.

9. Data Analysis Chart Types

10. 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!

11. 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

12. 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

13. 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

14. 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

15. Year
# of HR
1918 11
1919 29
1920 54
1921 59
1922 41
1923 46
1924 47
1925 60
1926
1927
1928 49
1929
Example
What is the mean, median and mode of the data?
Mean 45.2
Median46.5
Mode46

16. 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

17. Frequency Distribution Activity
Get into partners and complete the following with your specific data set:
Find the mean, median, and Mode

18. Box and Whisker Plot Measures of Variability QuartilesQ1, Q2 , Q3
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

19. 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?

20. Box and Whisker Plot
82, 78, 94, 68, 74, 88, 64, 42, 72, 82, 79, 99
Mean 77
Median 78
Mode 82
What are Q1, Q2 , Q3?
Q1=69
Q2=78
Q3=86
Interquartile Range 17
Semi-interquartile Range
8.5

21. 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

23. 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

24. Measures of Variability in Data Set
Mean Deviation
The average absolute value distance each piece of data is from the mean
Formula
MD=
What is the mean deviation of our example?

25. Mean Deviation Example
Recall previous box and whisker example:
82, 78, 94, 68, 74, 88, 64, 42, 72, 82, 79, 99
Find Mean Deviation

26. 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.

27. Measures of Variability in Data Set
Standard Deviation
Measures of the average amount each piece of data deviates from the mean
Formula

28. 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

29. Measures of Variability in Data Set
What is the variance and standard deviation for our test score example?
Variance
Standard Deviation

30. 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.

31. Measures of Variability in Frequency Distribution
Standard Deviation of the Data in a Frequency Distribution

32. Measures of Variability in Frequency Distribution
Variance of the Data in a Frequency Distribution
=δ2

33. 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?

34. 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

35. The Normal Distribution
About 95.2% of the data are within 2 standard deviations from the mean
About 68% of the data are within 1 standard deviation from the mean.
About 99.6% of the data are within 3 standard deviations from the mean

36. The Normal Distribution
Represents those values that fall between two and three standard deviations below the mean
Represents those values that fall between one and two standard deviations above the mean
Mean Value

37. 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 hour interval if there were a total of 2000 patients?
68.3%*(2000)=1366
How many patients healed in the hour interval if there were a total of 2000 patients?
1994

38. 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