Transcript Chapter 2
CHAPTER 2
Graphical Descriptions of Data
SECTION 2.1
Frequency Distributions
After collecting the data, we need to organize the data. This
chapter will describe different ways to organize the data.
ORDERED ARRAY
Arranging data from least to greatest or vice versa.
VOCABULARY
Grouped
Classes are ranges of possible
values
Ungrouped
Each class represents a single value
TWO TYPES OF FREQUENCY
DISTRIBUTIONS
STEPS TO CREATE A FREQUENCY DISTRIBUTION
Step 1: Determine the number of classes.
Step 2: Choose an appropriate class width.
Normally between 5 and 20, but the classes will be suggested in this lesson.
Find the range, then round up. The class width is the difference between lower
limits.
Step 3: Find the class limits.
The lower limit is the smallest number that can belong to the class.
The upper limit is the largest number that can belong to the class.
Step 4: Determine the frequency of each class.
Make a tally mark for each piece of data in the appropriate class, then count the
tally marks to find the total frequency for each class.
EXAMPLE
Class width =
2499−859
6
= 273.33 = 274. 𝑅𝑜𝑢𝑛𝑑 𝑡𝑜 $300 𝑡𝑜 𝑎𝑝𝑝𝑒𝑎𝑙 𝑡𝑜 𝑎𝑢𝑑𝑖𝑒𝑛𝑐𝑒.
Note: Round in increments of 50 for large data values. Used rounded number for smaller data values.
The class boundaries split the difference in the gap between the
upper limit of one class and the lower limit of the next class.
To find the class boundary, add the upper limit of one class to the
lower limit of the next class and divide by two.
Example:
𝑈𝑝𝑝𝑒𝑟 𝑙𝑖𝑚𝑖𝑡 = 10
𝐿𝑜𝑤𝑒𝑟 𝑙𝑖𝑚𝑖𝑡 = 11
CLASS BOUNDARIES
10+11
2
= 10.5
The class midpoint is the midpoint of the lower limit and the upper
limit.
To find the class midpoint, add the lower and upper limit of the
same class, then divide by 2.
Example:
Lower limit = 800
Upper limit = 1099
CLASS MIDPOINTS
800+1099
2
= 949.5
Relative frequency is the percentage of the data that falls in a
particular class.
Sample size is the total amount of data values.
RELATIVE FREQUENCY
Cumulative frequency is the sum of the frequency for a given
class and the frequencies of all previous classes.
The cumulative frequency of the last class should equal the
sample size.
CUMULATIVE FREQUENCY
PRACTICE PROBLEM
SOLUTION
SECTION 2.2A
Graphical Displays of Data: Pie Charts and Bar Graphs
Expense (in dollars)
4%
18%
27%
17%
34%
PIE CHART
Rent
Food
Car
Entertainment
Other
PARETO CHART
A bar graph that puts the data in descending order.
Represents two sets of data, with bars next to each other.
SIDE-BY-SIDE BAR GRAPH
STACKED BAR GRAPH
Represents two sets of data by stacking the bars.
SECTION 2.2B
Graphical Displays of Data: Histograms, Polygons, and Stem and Leaf Plots
RELATIVE FREQUENCY HISTOGRAM
Similar to the histogram, except the height of the bars is the
relative frequency instead of the frequency.
HOW TO CREATE A FREQUENCY POLYGON
Step 1: Mark the class boundaries on the x-axis and the
frequencies on the y-axis. There will be two extra classes, one on
the lower end and one on the upper end, both with a frequency
of 0.
Step 2: Add the midpoint to the x-axis, then plot a point at the frequency right above
the midpoint.
Step 3: Join each point with a line segment.
An ogive is a line graph that uses the boundaries and the cumulative frequency of
the data.
OGIVE (“OH-JIVE”)
OR
DOT PLOT
Similar to the stem and leaf other than it is a number line with dots representing the
leaves.
SECTION 2.3
Analyzing Graphs
Time-Series Graph – a picture of how data changes over time and has a variable of
time as the horizontal axis.
Cross-Sectional Graph – a picture of the data at a given moment in time. Neither axis will
have a variable of time