Frequency Distribution

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).

Question

� How do we construct a frequency distribution table?

Let’s Try!!! � Ages of 50 men randomly selected from a population who died in gunfire are given. Construct a frequency distribution table having 7 classes.

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

Determine the range. R = Highest Value – Lowest

Value R = 76 – 16 = 60

�  Find the class width (c).

kRc

classesofnumberRangewidthclass =⇔=

957.8760

===c

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

Classes Class boundaries

Tally Marks Freq. x

70 – 78 61 – 69 52 – 60 43 – 51 34 – 42 25 – 33 16 – 24

69.5 – 78.5 60.5 – 69.5 51.5 – 60.5 42.5 – 51.5 33.5 – 42.5 24.5 – 33.5 15.5 – 24.5

///// ///// // /////-// /////-/////-//// /////-/////-/////-//

5 5 0 2 7 14 17

74 65 56 47 38 29 20

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

� 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.

� STEP 3. Find the class width by dividing the range by the number of classes.

(Always round – off )

kRc

classesofnumberRangemarkclassorwidthclass

=⇔

=

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

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.

� All classes 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.

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?

SLOPE

SLOPE

Slope is a measure of steepness

Types of Slope

Positive Negative

Zero

Undefined or

No Slope

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

x2 – x1

Find the slope of the line through the

points (3,7) and (5, 19). x1 y1 x2 y2

m = 19 – 7

5 – 3 m = 12 2

m = 6

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

If given an equation of a line, there are 2 ways to find the

slope and y-intercept.

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

slope y-intercept

Find the slope and y-intercept of the

following equations.

y = 3x + ½ slope= 3

y-intercept = ½

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

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

Find the slope and y-intercept of the

following equations.

8x + 11y = 7 A B C

m= -8/11 b = 7/11

-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

If given the graph of a line, find the

slope by using the “triangle” method to

find the rise over run.

rise = 4

run = 5

m= rise run

m= 4/5

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The End