A Presentation A Presentation On Chapter – On Chapter – 14 (Statistics).14 (Statistics).

What is statistics?What is statistics?

a branch of mathematics that provides techniques a branch of mathematics that provides techniques to analyze whether or not your data is significant to analyze whether or not your data is significant (meaningful)(meaningful)

Statistical applications are based on probability Statistical applications are based on probability statementsstatements

Nothing is “proved” with statisticsNothing is “proved” with statistics Statistics are reportedStatistics are reported Statistics report the probability that similar results Statistics report the probability that similar results

would occur if you repeated the experimentwould occur if you repeated the experiment

Mean – arithmetic average = Σx/n

Median – the halfway point

Mode – the most common answer

Looking at profile of data: Looking at profile of data: DistributionDistribution

• What is the frequency of distribution, What is the frequency of distribution, where are the data points? where are the data points?

Class (height of plants-cm)Class (height of plants-cm) Number of plants in each classNumber of plants in each class

0.0-0.90.0-0.9 33

1.0-1.91.0-1.9 1010

2.0-2.92.0-2.9 2121

3.0-3.93.0-3.9 3030

4.0-4.94.0-4.9 2020

5.0-5.95.0-5.9 1414

6.0-6.96.0-6.9 22

Distribution Chart of Heights of 100 Control Plants

Distribution Chart of Heights of 100 Control Plants

Mode and MedianMode and Median

Mode: most frequently seen value (if no Mode: most frequently seen value (if no numbers repeat then the mode = 0)numbers repeat then the mode = 0)

Median: the middle number Median: the middle number If you have an odd number of data then the If you have an odd number of data then the

median is the value in the middle of the setmedian is the value in the middle of the set If you have an even number of data then the If you have an even number of data then the

median is the average between the two median is the average between the two middle values in the set.middle values in the set.

Frequency Distribution Frequency Distribution

lists classes (or categories) of values, along lists classes (or categories) of values, along

with frequencies (or counts) of the number with frequencies (or counts) of the number

of values that fall into each classof values that fall into each class

2-1 Frequency Distributions

Ogive

Upper Class Limit(points are plotted at the upper right corner of each bar in the histogram)

MeanMean

(Arithmetic Mean)(Arithmetic Mean)

AVERAGEAVERAGE

the number obtained by adding the values the number obtained by adding the values and dividing the total by the number of and dividing the total by the number of

valuesvalues

Definitions

Statistical Computations (the Math)Statistical Computations (the Math)

If you are using a sample populationIf you are using a sample population• Arithmetic Mean (average)Arithmetic Mean (average)

The sum of all the scores divided by the total number of scores.

Definitions MedianMedian

the middle value when the original the middle value when the original data values are arranged in order of data values are arranged in order of increasing (or decreasing) magnitudeincreasing (or decreasing) magnitude

not affected by an extreme value~

use class midpoint of classes for variable x

Mean from a Frequency Table

x = class midpoint

f = frequency

Σ f = n

x = f

Σ (x • f)Σ

Mean by Three MethodsMean by Three Methods

• By Direct Method= By Direct Method= fi.xi fi.xi fi fi • By Assumed Method=a+ By Assumed Method=a+ fi.difi.di fi fi • By Step Deviation Method=a+ By Step Deviation Method=a+ fi.ui fi.ui X iX i fifi

Formula To Find Formula To Find ModeMode

Mode=Highest Frequency=f1, class Mode=Highest Frequency=f1, class Preceding to f1 = f0, class succeeding to Preceding to f1 = f0, class succeeding to fi= f2, Lower Value in which f1 Lies, h= fi= f2, Lower Value in which f1 Lies, h= class intervals.class intervals.

Mode= l+ Mode= l+ f1 – f0f1 – f0 X h X h

2f1 – f0 – f22f1 – f0 – f2

Formula to find MedianFormula to find Median

Median= n=total no. of observations; Median= n=total no. of observations; divided by 2; becomes=divided by 2; becomes=n n , ,

22 l =Lower Limit in which n lies, fi= class in l =Lower Limit in which n lies, fi= class in

which n lies, c.f.= class preceding fi, h= which n lies, c.f.= class preceding fi, h= class intervals.class intervals.

Median= Median= nn _ c.f. _ c.f. l+ l+ 22_________ X h_________ X h fifi

Histogram-Frequency Distribution Histogram-Frequency Distribution ChartsCharts

This is called a “normal” curve or a bell curveThis is an “idealized” curve and is theoretical based on an infinite number derived from a sample

1) Statistics are useful for figuring out random noise from real effects

2) Numbers are not absolute, and they can be easily manipulated

3) Always scrutinize data closely, and draw your own conclusions.

4) 85% of all statistics are made up on the spot: the rest are all wrong