1. Definitions Data: A collection of information in context.
DAY 1
Definitions
Data: A collection of information in context.
Population: A set of individuals that we wish to describe and/or make predictions about.
Individual: Member of a population.
Variable: Characteristic recorded about each individual in a data set.

2. Be sure to label the graph and use proper scales.
Types of Data
Categorical – places individuals into groups (sometimes referred to as qualitative)
Example: gender, eye color, zip code, dominant hand
Quantitative – consists of numerical values (it makes sense to find an average)
Example: height, weight, income, vertical leap
Graphs for Categorical data are Bar graphs and Pie charts
Be sure to label the graph and use proper scales.

3. Example 1: Reading and Interpreting Bar Graphs
Use the graph to answer each question.
A. Which casserole was ordered the most?
B. About how many total orders were placed?
C. About how many more tuna noodle casseroles were ordered than king ranch casseroles?
D. About what percent of the total orders were for baked ziti?

4. Use the graph to answer each question.
Check It Out! Example 1
Use the graph to answer each question.
a. Which ingredient contains the least amount of fat?
b. Which ingredients contain at least 8 grams of fat?

5. Example 2: Reading and Interpreting Double Bar Graphs
A double-bar graph __________________________________________
____________________________________________________________________________________________
Example 2: Reading and Interpreting Double Bar Graphs
Use the graph to answer each question.
A. Which feature received the same satisfaction rating for each SUV?
B. Which SUV received a better rating for mileage?

6. Check It Out! Example 2
Use the graph to determine which years had the same average basketball attendance. What was the average attendance for those years?

7. Tips for Making a Bar Graph

9. Making a Bar Graph
Here are the distributions for car colors in North America in 2008.
Color Percent of Vehicle
White 20
Black 17
Silver 17
Blue 13
Gray 12
Red 11
Beige/Brown 5
Green 3
Yellow/Gold 2
a.) What percent of vehicles had colors others than those listed?
b.) Display the data in a bar graph.
c.) Would it be appropriate to make a pie chart? If not explain why. If it is appropriate for this data then create one.

10. Tips for Making the Pie (or Circle) Graph
You must convert the __________________by multiply the percent value by_______.
Draw a radius somewhere on the circle and start there and work your way around the circle counter-clockwise until you get back to the radius you started with.

11. Color Percent of Vehicle
White 20
Black 17
Silver 17
Blue 13
Gray 12
Red 11
Beige/Brown 5
Green 3
Yellow/Gold 2

12. Measuring Centers Mean (“average”) – Median – Mode –
X =
X1 + X2 + X3 + … + Xn n
Sum of observations
Number of observations =
Median –
1.) Place data in numerical order
2.) If there are an odd number of observations, the median is the center observation in the ordered list.
3.) If there are an even number of observations, the median is the average of the two center observations in the ordered list.
Mode –
It helps if you put the data into numerical order. (STAT, edit, enter numbers, STAT, sortA(, enter, 2nd (1 or 2), enter. Go back to list and the numbers will be in order.

13. If the Mean, Median and Mode for the following observations
78, 98, 48, 63, 84, 100, 95, 86, 91 ,87, 48, 94, 94, 89 ,95, 95, 97, 41 ,65, 85
Mean = 20 =
Median: 41, 48, 48, 63, 65, 78, 84, 85, 86, 87, 89, 91, 94, 94, 95, 95, 95, 97, 98, 100
median is = 88 2
Mode is 95

14. Use the data set below to complete each table
Measure of Center
Brief Definition
Value
Mean
Median
Mode

15. 1. The weights in pounds of six members of a basketball team are 161, 156, 150, 156, 150, and Determine the mean, median, mode and range of the data set.

16. End of Day 1

17. Graphs for Quantitative Data
Dotplots –
Box and Whisker –

18. Dotplots
A dotplot is a graph where dots are used to represent individual data points.
The dots are plotted above a number line.
Dotplots can be used to represent frequencies for categorical or quantitative data.
Dotplots can be used to see how data items compare.

19. Draw a Dotplot
Draw a dotplot for the data set below. 25, 25, 20, 25, 16, 20, 25, 30, 25, 31, 26, 28, 30

20. Box and Whiskers

21. Finding First and Third Quartile
The first quartile lies one quarter of the way up the list. (25% of the data is below the first quartile.)
The third quartile lies three quarters of the way up the list. (75% of the data is below the third quartile.)
1.) Find the median to divide the data is half.
2.) Find the “median” of the lower half, this point will be the first quartile.
3.) Find the “median” of the upper half, this point will be the third quartile.
***In the case of two data points being either the first or third quartiles, then use same method as the median (add together and divide by 2)

22. Measures of Spread How much do values typically vary from the center?
Range – Interquartile Range (IQR)

23. Use the data to make a box-and-whisker plot.
13, 14, 18, 13, 12, 17, 15, 12, 13, 19, 11, 14, 14, 18, 22, 23

24. Find the minimum, maximum, median (Q2), lower quartile (Q1), and upper quartile (Q3) for the following sets of data and draw the Box and Whisker plot (or Boxplot)
32, 40, 35, 29, 14, 32
6, 1, 7, 6, 5, 5, 0, 1, 0, 8, 4
121, 143, 98, 144, 165, 118

25. Now, check the previous data for outliners.
Checking for Outliers
An outlier is data point that is extremely far away from the rest of the data and may effect some of the measurements we take from that data.
An outlier is any point that is farther than 1.5 x the IQR from the first or third quartile.
Now, check the previous data for outliners.

26. Find any outliers, if any.
32, 40, 35, 29, 14, 32
6, 1, 7, 6, 5, 5, 0, 1, 0, 8, 4
121, 143, 98, 144, 165, 118

27. Examples
Identify the outlier in the data set {16, 23, 21, 18, 75, 21} and determine how the outlier affects the mean, median, mode, and range of the data. outlier: _________________
with the outlier without the outlier

28. End of Day 2

29. Graphs for Quantitative Data
DAY 2
Graphs for Quantitative Data
Stem and Leaf Plots – The stem is the larger
place value and the leaves are the smaller
place values. This graph is used to give a
description of the distribution while using
the actual values. Important to have a key
for the reader.
Histograms –

30. Example 1A: Making a Stem-and-Leaf Plot
The numbers of defective widgets in batches of 1000 are given below. Use the data to make a stem-and-leaf plot.
14, 12, 8, 9, 13, 20, 15, 9, 21, 8, 13, 19
Number of Defective
Widgets per Batch
The tens digits are the _________.
The ones digits are the _________.
List the leaves from ___________ to
_____________ within each row.
Stem Leaves
Key: 1|9 means 19
Title the graph and add a key.

31. Example 1B: Making a Stem-and-Leaf Plot
The season’s scores for the football teams going to the state championship are given below. Use the data to make a back-to-back stem-and-leaf plot.
Team A: 65, 42, 56, 49, 58, 42, 61, 55, 45, 72
Team B: 57, 60, 48, 49, 52, 61, 58, 37, 63, 48
Team A’s scores are on the left side
and Team B’s scores are on the
right.
Team A Team B 3 4 5 6 7
The _________ digits are the stems.
The _________ digits are the leaves.
Title the graph and add a key.
Key:

32. Check It Out! Example 1 Stem Leaves
The temperature in degrees Celsius for two weeks are given below. Use the data to make a stem-and-leaf plot.
7, 32, 34, 31, 26, 27, 23, 19, 22, 29, 30, 36, 35, 31
Stem Leaves

33. The frequency of a data value is ___________________
______________________________________________
A frequency table ______________________________

34. Example 2: Making a Frequency Table
The numbers of students enrolled in Western Civilization classes at a university are given below. Use the data to make a frequency table with intervals.
12, 22, 18, 9, 25, 31, 28, 19, 22, 27, 32, 14
Step 1: ___________________________________
Step 2: ____________________________________________________

35. Example 2 Continued 1-10 1 11-20 4 21-30 5 31-40 2
Step 3: ________________________________________
_______________________________________________
Enrollment in Western
Civilization Classes
Number Enrolled
Frequency
1-10 1
11-20 4
21-30 5
31-40 2

36. Check It Out! Example 2
The number of days of Maria’s last 15 vacations are listed below. Use the data to make a frequency table with intervals.
4, 8, 6, 7, 5, 4, 10, 6, 7, 14, 12, 8, 10, 15, 12
Step 1: Identify the least and greatest values.
Step 2: Divide the data into equal intervals.

37. Check It Out! Example 2 Continued
Step 3: List the intervals in the first column of the table. Count the number of data values in each interval and list the count in the last column. Give the table a title.
Interval
Frequency

38. What Is a Histogram?
A histogram is a bar graph that shows the distribution of data.
A histogram is a bar graph that represents a frequency table.
The horizontal axis represents the intervals.
The vertical axis represents the frequency.
The bars in a histogram have the same width and are drawn next to each other with no gaps.

39. Constructing a Histogram
Step 1 - Count number of data points
Step 2 - Compute the range
Step 3 - Determine number of intervals (5-12)
Step 4 - Compute interval width
Step 5 - Determine interval starting & ending points
Step 6 - Summarize data on a frequency table
Step 7 - Graph the data

40. Example 3: Making a Histogram
A histogram is __________________________________________
_______________________________________________________
Use the frequency table in Example 2 to make a histogram.
Enrollment in Western
Civilization Classes
Step 1: _____________________
____________________________
Number Enrolled
Frequency
1 – 10 1
11 – 20 4
21 – 30 5
31 – 40 2

41. Example 3 Continued
Step 2: ______________________________________________
_____________________________________________________
All bars should be the same width.
The bars should touch, but not overlap.
Step 3: _______________________________________________

42. Number of Vacation Days
Check It Out! Example 3
Make a histogram for the number of days of Maria’s last 15 vacations.
4, 8, 6, 7, 5, 4, 10, 6, 7, 14, 12, 8, 10, 15, 12
Step 1: Use the scale and interval from the frequency table.
Number of Vacation Days
Interval
Frequency
4 – 6 5
7 – 9 4
10 – 12
13 – 15 2

43. The data below shows the number of hours per week spent playing sports by a group of students.
What is the minimum, maximum, & range?
Make a frequency tables using intervals you decide on.
Draw a histogram. 2 7 17 9 6 13 8 4 5 12 3 11 1 15

44. Hours per week playing sports Frequency
Hours per week playing sports
Frequency

45. End of Day 3 Quiz tomorrow

46. Describing Distributions
Center
Shape
Spread
Outliers

47. Center
For describing the center of the data, we can use either the Median or the Mean.
Both are useful, in cases where the data is skewed one way the Median is a better choice because it is more resistant to outliers.

48. Shape
“Symmetrical/Normal”
“Skewed Left”
“Skewed Right”

49. Shape

50. Spread
Even though we are not graphing a Box and whisker we still use these two measures of spread.
Range - is the difference of the maximum and minimum value - spread of the entire data set
Interquartile Range (IQR) - is the difference of the upper quartile (Q3) & the lower quartile (Q1) – spread of the middle 50% of the data
We can also use the Standard deviation

51. Standard Deviation is another measure of spread
DAY 6
Standard Deviation
is another measure of spread
is the typical amount that a data value will vary from the mean
the larger the standard deviation, the ______ ________________the data set (the data points are far from the mean )
the smaller the standard deviation, the ______ _______________ the data set (the data points are clustered closely around the mean.)

52. Calculating Standard Deviation
Step 1 –
Step 2 –
Step 3 –
Step 4 –
Step 5 –
Step 6 –

53. Standard Deviation Find the standard deviation for this set of data.
3, 5, 5, 7, 8, 9, 9, 10
mean =
variance =
standard =
deviation
Value
Deviation from mean
Squared Deviation 3 5 7 8 9 10
3 – 7 =-4
5 – 7 =
5 – 7 = -2
7 – 7 = 0
8 – 7 = 1
9 – 7 = 2
10 – 7 = 3 16 4
= 42 = 6
(8 – 1) 9
√6 = 2.45

54. Find the Standard Deviation for the Following Data
Example #1 1, 3, 4, 4, 4, 5, 7, 8, 9 Example #2 338, 318, 353, 313, 318, 326, 307, 317 Remember to find the mean first.
Standard deviation = 2.55
Standard deviation = 14.99

55. The owner of the Ches Tahoe restaurant is interested in how much people spend at the restaurant.  He examines 10 randomly selected receipts for parties of four and writes down the following data. Find the standard deviation.
44,   50,   38,   96,   42,   47,   40,   39,   46,   50

56. Practice Problem #1: Calculate the standard deviation of the following test data by hand. Use the chart below to record the steps.
Test Scores: 22, 99, 102, 33, 57, 75, 100, 81, 62, 29

57. Standard Deviation
Find the standard deviation for this set of data. 2, 3, 5, 5, 7, 8, 9, 9, 10, 12 mean = variance = standard = deviation
Value
Deviation from mean
Deviation Squared 2 3 5 7 8 9 10 12

58. Practice!
Find the standard deviation for this set of data. 6, 12, 4, 13, 7, 12, 11, 5 mean = variance = standard = deviation
Value
Deviation from mean
Deviation Squared 6 12 4 13 7 11 5

59. End of Day 5 Project tomorrow