Frequency Distribution
Jan 21, 2015
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