introduction to statistical concepts.pptx

8/22/2019 Introduction to Statistical Concepts.pptx

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Statistics plays a very

important role in measurement andevaluation. Statistical techniquesallow us to describe the

performance of our students andmake proper scientific inferencesabout their performance. This

chapter introduces the students tosome very basic concepts in

Statistics.


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Statistics is a scientific body of

knowledge that deals with:

Collection of dataOrganization or presentation ofdata

Analysis and interpretation ofdata

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Introduction

toStatisticalConcepts

The Idea ofRandomnes

Measures ofCentral

Tendency

TheStandard

Deviation

FrequencyDistribution

Table

Measures ofLocation and

Fractiles


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Populationidentifies the totality of(P) objects under investigation.

refers to a large collectionof objects, places or things.

Samplesmall portion or part of a(S) population.

- a representative of a

population in a research study.


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Population

Sample


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Let us consider a group of thirty (30)students whose examination scores are as

follows:P={15,20,25,25,30,35,26,14,17,18,12,15,22,27,33,3

2,21,18,18,13,14,21,17,18,19,23,22,21,26,31}

Now, the teacher randomly selects fifteen(15)examination scores for further analysis andobtains:S= {20,15,14,12,33,18,21,17,22,21,26,30,32,13,15}

The idea of randomnessunpredictability.


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While the mean is a good singledescription of the location of the central

tendency of the data, it is often not enough tofully describe the data sets. A measure ofdispersion or scatter is also needed. The

standard deviation is a measure of theaverage deviation or departure of theindividual scores from the mean and is given

by:


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Mean (or average) is equal to the sum of

all values in the data set divided by the numberof values in the data set.

Mean of PopulationP= (15++31)/ 30 = 648/30 = 21.60

Mean of SampleS= (20+ +15)/15 = 319/15 = 21.27

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For grouped data:


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Median- is the set of numbersarranged in order of magnitude is either themiddle value or the arithmetic mean of the2 middle values.Where:

LB- lower bound of the middle classn- the number of the observations

F- cumulative frequency of the class previous

to the middle class

f- is the frequency of the middle class- the size of the modal class interval


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Mode - is the value which occurs withthe greatest frequency.

for grouped data:Where:

LB- Lower bound of the middle class

d1- the difference between the modalfrequency and the frequency of the next

lower class

d2- is the difference between the modal

frequency and the frequency of the nexthighest class.

- the size of the modal class interval


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Steps in Constructing Frequency Distribution TableStep 1: Determine the range

R = Highest Value Lowest Value

Step 2: Determine the tentative number of classes (k)k = 1+3.322 log N - always round off

Step 3: Find the class width by dividing the range by the

number of classes.Class width = range/ number of classes or c = R/k


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77,77,78,80,80,80,80,81,82,82,82,82,83,83,83,83,83,84,84,84,84,84,84,84,84,87,87,87,87,87,88,

88,88,88,88,88,89,89,89,89,91,91,91,91,93,94,94,94,95,97

R = Highest value lowest value

= 97-77R = 20

k = 1 + 3.322logN= 1 + 3.322 log50

= 1 + 5.6

k = 6.64 or 7

Class width = R/k

= 20/7C= 2.86 or 3


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(Final Grade) (f) (CB) (x)

77

79 3 76.5

79.5 78

80 82 9 79.5 82.5 81

83 85 13 82.5 85.5 84

86 88 11 85.5 88.5 87

89 91 8 88.5 91.5 90

92

94 4 91.5

94.5 93

95 97 2 94.5 97.5 96

f = 50


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(Final

Grade)(f) (CB) (x) (


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MEAN

=

M = 85.92

MEDIAN

=

Md = 85.5MODE

=

MO = 84.5


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Measures of Location or

Fractiles- values below which a specified fractionor percentage of the observations in a given setmust fall.

Percentiles (100)Deciles (10)Quartiles (4)


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Percentilesare values that divide a set ofobservations in an array into 100 equal parts.

For ungrouped:

Decilesare values that divide a set of

observations in an array into 10 equal parts.For ungrouped:

Quartilesare values that divide a set ofobservations in an array into 4 equal parts.

For ungrouped:


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Example: the ff. were the scores of 10

students. 2, 8, 6, 9, 7, 5, 8, 10, 10, 1. Findthe 64th percentile

= = 7.04 or 8

1, 2, 5, 6, 7, 8, 8, 9, 10, 10

64% of the scores are below 9


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Percentile from a Frequency Distribution

Where:

the Pith class is the class where the


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Age Frequency


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introduction to statistical concepts.pptx

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