1. CONSTRUCTION OF A FREQUENCY DISTRIBUTION
A grouping of data into categories showing the number of observations in each mutually exclusive category.

2. DISCRETE FREQUENCY DISTRIBUTION
The details regarding family number of children is given below, construct frequency distribution for the following data
2,3,4,1,1,0,2,3,4,0,1,3,2,4,0,1,2,2,2,3,2,3,1,1,1,0,1,2,3

3. 5 Steps To Organize Raw Data Into A Frequency Distribution
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5 Steps To Organize Raw Data Into A Frequency Distribution
Step 1: Decide on Number of Classes
Step 2: Determine The Class Interval
Step 3: Set The Individual Class Limits
Step 4: Tally The Data Into Classes
Step 5: Count The Tallies in Each Class & Present the Frequency Distribution
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4. Continuous Frequency Distribution
Ms. Kathryn Ball of AutoUSA wants to develop tables, charts, and graphs to show the typical selling price on various dealer lots. The table on the right reports only the price of the 80 vehicles sold last month at Whitner Autoplex.

5. EXAMPLE – Constructing Frequency Distributions: Quantitative Data

6. Constructing a Frequency Table - Example
Step 1: Decide on the number of classes.
A useful recipe to determine the number of classes (k) is the “2 to the k rule.” such that 2k > n.
There were 80 vehicles sold. So n = 80. If we try k = 6, which means we would use 6 classes, then 26 = 64, somewhat less than 80. Hence, 6 is not enough classes. If we let k = 7, then , which is greater than 80. So the recommended number of classes is 7.
Step 2: Determine the class interval or width.
The formula is: i  (H-L)/k where i is the class interval, H is the highest observed value, L is the lowest observed value, and k is the number of classes.
($35,925 - $15,546)/7 = $2,911
Round up to some convenient number, such as a multiple of 10 or 100. Use a class width of $3,000

7. Step 3: Set The Individual Class Limits
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Step 3: Set The Individual Class Limits
Classes must be mutually exclusive
Avoid overlapping or unclear class limits:
Include lower limit
Exclude upper limit
Example of class limits:
$12,000 up to $15,000 and $15,000 up to $18,000
$12,000 & $14,999 belong in the first class
$15,000 belongs in the second class
Avoid open ended classes (problems with graphing)
The lower limit of the first class should be a multiple of the class interval (not always possible)
Convenient multiples of ten are useful
You must compare the actual range to the range implied by the number of classes & class interval
General guidelines that are not always possible to follow. Thus, making Frequency Distributions is often refer to as an “art”.
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8. Constructing a Frequency Table - Example

9. Constructing a Frequency Table
Step 4: Tally the vehicle selling prices into the classes.
Step 5: Count the number of items in each class.

10. Relative Frequency Distribution
To convert a frequency distribution to a relative frequency distribution, each of the class frequencies is divided by the total number of observations.

11. Class Intervals and Midpoints
Class midpoint: A point that divides a class into two equal parts. This is the average of the upper and lower class limits.
Class frequency: The number of observations in each class.
Class interval: The class interval is obtained by subtracting the lower limit of a class from the lower limit of the next class.

12. Inclusive and Exclusive
Inclusive Classes: If upper limit of the classes are included in the class itself then that classes are called Inclusive classes.
Exclusive Classes: If upper limit of the classes are not included in the class itself then that classes are called Exclusive classes.

13. Class Boundaries and Class Limits
Class Boundaries: If upper limit of one class is equal to lower limit of next class then that is called class Boundaries.
Class Limits: If upper limit of one class is not equal to lower limit of next class then that is called class Limits.

14. Grouped Frequency Distributions Continuous Ratio/Interval Data
Divide the overall range of the Observed values into classes; Count the number of observations that fall into each class.
Example: Kenkel, pg.46, Monthly Salaries of employees at Lang’s Trucking Company

16. Histogram (For Quantitative data)
A frequency distribution based on quantitative data
A graph in which the classes are marked on the horizontal axis and the class frequencies on the vertical axis.
The class frequencies are represented by the heights of the bars and the bars are drawn adjacent to each other.

17. Frequency Polygon
A frequency polygon also shows the shape of a distribution and is similar to a histogram.
It consists of line segments connecting the points formed by the intersections of the class midpoints and the class frequencies.

18. Cumulative Frequency Distribution

19. Cumulative Frequency Distribution

20. Stem-and-Leaf Plots
Stem-and-Leaf Plots: A convenient method to display every piece of data by showing the digits of each number.

21. Stem and Leaf Plot – a visual way to display a large set of data
Stem – largest place value(s) of a number
Leaf – smallest place value of a number

22. Statistics: Stem-and-Leaf Plots
In a stem-and-leaf plot, the greatest common place value of the data is used to form stems.
The numbers in the next greatest place value position are then used to form the leaves.

23. Step 1: Find the least and the greatest number in the set of data.

24. Step 2: Draw a vertical line between the digit in the smallest place value of the number and the other digits of the number. This gives the high and low for the range of the stems.
least number 2
greatest number
2 3

25. Step 3: Make a chart with the titles STEM and LEAF.
STEM LEAF

26. Step 4: Write the digits that form the stem in the STEM column.
STEM LEAF
0 1 2

27. Step 5: Write the digits that form the leaf for each number in the LEAF column across from the STEM of the number.
STEM LEAF 2 4 5 9 3 8 9 3 3 4 1 8 4 3 1 3 9 6 2 5 6 9 2 3 1

28. Age of United states Presidents at their First Inauguration: (Through the 40th presidency)
Stem
Leaf 4 5 6 9 8 6 9 7 2 3 7 7 7 8 7 4 1 2 6 4 5 4 1 6 5 1 4 1 5 6 2 1 1 8 4 5 2 1 9 4

29. Statistics: Stem-and-Leaf Plots
Age of United states Presidents at their First Inauguration: (Through the 40th presidency)
Rearrange the leaf in numerical order from least to greatest
Stem
Leaf 4 5 6

30. Statistics: Stem-and-Leaf Plots
It is easy to interpret or analyze information from the Stem-and-Leaf.
How many presidents were 51 years old at their inauguration?
What age is the youngest president to be inaugurated?
What is the age of the oldest president to be inaugurated?
How many presidents were years old at their inauguration? 4 42 69 7
Stem
Leaf: Age of United States Presidents at their First Inauguration
(through the 40th Presidency) 4 5 6