frequency distribution
DESCRIPTION
stats Frequency DistributionTRANSCRIPT
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Frequency Distribution
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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).
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Question
� How do we construct a frequency distribution table?
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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.
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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
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Determine the range. R = Highest Value – Lowest
Value R = 76 – 16 = 60
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� Find the class width (c).
kRc
classesofnumberRangewidthclass =⇔=
957.8760
===c
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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
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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
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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
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� 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.
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� STEP 3. Find the class width by dividing the range by the number of classes.
(Always round – off )
kRc
classesofnumberRangemarkclassorwidthclass
=⇔
=
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� STEP 4. Determine the frequency for each class by referring to the tally columns and present the results in a table.
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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.
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� 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.
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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?
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SLOPE
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SLOPE
Slope is a measure of steepness
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Types of Slope
Positive Negative
Zero
Undefined or
No Slope
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If given 2 points on a line, you may find the slope using the formula m = y2 – y1
x2 – x1
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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
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Find the slope (3, 4) and (-6, -2)
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If given an equation of a line, there are 2 ways to find the
slope and y-intercept.
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One method is to write the equation in slope-intercept form, which is y = mx + b.
slope y-intercept
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Find the slope and y-intercept of the
following equations.
y = 3x + ½ slope= 3
y-intercept = ½
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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
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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
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Find the slope and y-intercept of the
following equations.
8x + 11y = 7 A B C
m= -8/11 b = 7/11
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-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
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If given the graph of a line, find the
slope by using the “triangle” method to
find the rise over run.
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rise = 4
run = 5
m= rise run
m= 4/5
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MET’s Institute of Management, Bhujbal Knowledge City, Adgaon, Nashik
1. Name of the student: 2 . Graduation in: 3. Please tick whether you had learnt statistics in your
graduation level: Yes \ No 4. Please grade yourself according to you in which category you lie in the knowledge of mathematics and statistics 1.Poor 2. Not good 3.Average 4.Good
5.Excellent
Feedback form
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5. Whether Induction on basics of Mathematics and Statistics was fruitful
for you ? Yes / No If Yes then please state why? 6. Do you need any change in the current
teaching methodology adopted for statistics? 7. Any suggestions related to the subject statistics:
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The End
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