frequency distribution

Frequency Distribution

Frequency DistributionA 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 2523 25 21 33 65 17 20 7647 69 20 31 18 24 35 2417 36 65 70 22 2565 1624 29 42 37 26 46 27 6321 27 23 25 71 37 75 2527 23

Determine the range.

R = Highest Value – Lowest

Value

R = 76 – 16 = 60

Find the class width (c).

k

Rc

classesofnumber

Rangewidthclass

957.87

60c

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 boundarie

s

Tally Marks Freq.

x

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

69.5 – 78.560.5 – 69.551.5 – 60.5 42.5 – 51.533.5 – 42.524.5 – 33.515.5 – 24.5

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

5 5 0 27

14 17

74655647382920

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 )

k

Rc

classesofnumber

Rangemarkclassorwidthclass

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

PositiveNegative

Zero

Undefinedor

No Slope

If given 2 points on a line, you may findthe slope using theformula 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 equationof a line, there are2 ways to find the

slope and y-intercept.

One method is towrite the equation inslope-intercept form,which is y = mx + b.

slopey-intercept

Find the slope andy-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 tofind the slope if givenan equation of a line

is to write the equationin the form Ax + By = C.

m = -A/B, b = C/B

Find the slope andy-intercept of the

following equations.

8x + 11y = 7A 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/-2m= -3 b = -7

If given the graphof 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