This document provides an overview of frequency distributions and how to construct a frequency distribution table from a set of data. It discusses the key steps: 1) determining the range of the data, 2) choosing the number of classes, 3) calculating the class width, and 4) tallying the frequency of observations within each class interval to populate the table. Guidelines for constructing frequency tables are also outlined, such as using mutually exclusive and exhaustive class intervals of uniform width. An example of constructing a 7-class frequency table from a set of 50 observations is shown to demonstrate the process.

1. Frequency Distribution

2. Frequency Distribution
— A representation,
in a tabular format,
which displays the number of
observations within a given interval. The
intervals must be mutually exclusive (each
score must belong to exactly one class)
and exhaustive (Including every possible
element).

3. Question
— Howdo we construct a
frequency distribution
table?

4. Let’s Try!!!
— Agesof 50 men randomly
selected from a population
who died in gunfire are given.
Construct a frequency
distribution table having 7
classes.

5. 19 18 30 40 41 33 73 25
23 25 21 33 65 17 20 76
47 69 20 31 18 24 35 24
17 36 65 70 22 25 65 16
24 29 42 37 26 46 27 63
21 27 23 25 71 37 75 25
27 23

6. Determine the range.
R = Highest Value – Lowest
Value
R = 76 – 16 = 60

7. — Find the class width (c).
Range R
class width = ⇔ c=
number of classes k
60
c = = 8.57 = 9
7

8. Write the classes starting with lowest
score.
Classes Tally Marks Freq.
70 – 78
61 – 69
52 – 60
43 – 51
34 – 42
25 – 33
16 – 24

9. Classes Class Tally Marks Freq. x
boundaries
70 – 78 69.5 – 78.5 ///// 5 74
61 – 69 60.5 – 69.5 ///// 5 65
52 – 60 51.5 – 60.5 0 56
43 – 51 42.5 – 51.5 // 2 47
34 – 42 33.5 – 42.5 /////-// 7 38
25 – 33 24.5 – 33.5 /////-/////-//// 14 29
16 – 24 15.5 – 24.5 /////-/////-/////-// 17 20

10. General Process of
Constructing a Frequency
Table
— STEP 1: Determine the
range.
Range (R)= Highest Value – Lowest
Value
Example in data: 29,55,65,23,45,86,44
Find Range

11. — STEP
2. Determine the tentative
number of classes (k)
— Note:
— These classes are usually specified in
question.
— The number of classes should be between 5
and 20. The actual number of classes may
be affected by convenience or other
subjective factors.

12. — STEP 3. Find the class width by
dividing the range by the number
of classes.
Range
class width or class mark =
number of classes
R
⇔ c=
k
(Always round – off )

13. — STEP 4. Determine the
frequency for each class by
referring to the tally columns
and present the results in a table.

14. When constructing frequency
tables, the following guidelines
should be followed.
— The classes must be mutually
exclusive. That is, each score
must belong to exactly one
class.
— Include all classes, even if the
frequency might be zero.

15. — Allclasses should have the
same width, although it is
sometimes impossible to avoid
open – ended intervals such as
“65 years or older”.
— The number of classes should
be between 5 and 20.

16. Using Table:
— What is the lower class limit of
the highest class? Upper class
limit of the lowest class?
— Find the class mark of the class
43 – 51.
— What is the frequency of the
class 16 – 24?

17. SLOPE

18. SLOPE
Slope is a measure of
steepness

19. Types of Slope
Zero
Negative
Positive Undefined
or
No Slope

20. If given 2 points on
a line, you may find
the slope using the
formula m = y2 – y1
x2 – x1

21. Find the slope of the
line through the
points (3,7) and (5, 19).
x1 y1 x2 y2
m = 19 – 7 m = 12 m=6
5–3 2

22. Find the slope
(3, 4) and (-6, -2)

23. If given an equation
of a line, there are
2 ways to find the
slope and y-intercept.

24. One method is to
write the equation in
slope-intercept form,
which is y = mx + b.
slope
y-intercept

25. Find the slope and
y-intercept of the
following equations.
y = 3x + ½
slope= 3
y-intercept = ½

26. 3x + 5y = 10
First, solve the equation for y.
3x + 5y = 10
5y = -3x + 10
y = -3/5 x + 2
m= -3/5 b=2

27. Another method to
find the slope if given
an equation of a line
is to write the equation
in the form Ax + By = C.
m = -A/B, b = C/B

28. Find the slope and
y-intercept of the
following equations.
A B C
8x + 11y = 7
m= -8/11 b = 7/11

29. -6x = 2y + 14
First, rewrite the equation in
the form Ax + By = C.
-6x - 2y = 14
m= 6/-2 b = 14/-2
m= -3 b = -7

30. If given the graph
of a line, find the
slope by using the
“triangle” method to
find the rise over run.

31. rise = 4
m= rise
run
run = 5 m= 4/5

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