Statistics ppt

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Statistics is the study of the collection, analysis, organization, interpretation, and presentation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments.

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In Class IX, you have studied the classification of given data ungrouped as well as grouped frequency distributions.You have also learnt to represent the data pictorially in the form of various graphs such as bar graphs,histograms and frequency polygons.In fact,you went a step further by studying certain numerical representatives of the ungrouped data,also called measures of central tendency,namely Mean,median and mode.In this chapter,we shall extend the study of these three measures,i.e.,mean,median and mode from ungrouped data to that of the grouped data.We shall also discuss the concept of Cumulative frequency,the cumulative frequency distribution and how to draw cumulative frequency curves, called ogives. INTRODUCTION

The mean for grouped data can be found by: :

The mean for grouped data can be found by: The direct method : The assumed mean method : The step deviation method :

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The mean(or average) of observations,as we know,is the sum of the values of all the observations divided by the total number of observations.From Class IX,recall that if x 1 , x 2 ,....,x n are observations with respective frequencies f 1 , f 2 ,...., f n ,then this means observation x 1 occurs f 1 times, x 2 occurs f 2 times,and so on.Now,the sum of the values of all the observations = f 1 x 1 + f 2 x 2 +....+ f n x n , and the number of observations = f 1 + f 2 +....+ f n .So, the mean x of the data is given by Recall that we can write this in short form by using the Greek letter ∑(capital sigma) which means summation.That is,

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The marks obtained by 30 students of Class X of a certain school in aMathematics paper consisting of 100 mark s are presented in table below. Find the mean of the marks obtained by the students.

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Now, for each class-interval, we require a point which would serve as the representative of the whole class. It is assumed that the frequency of each class interval is centred around its mid-point . So the mid-point (or class mark ) of each class can be chosen to represent the observations falling in the class. Recall that we find the mid-point of a class (or its classmark) by finding the average of its upper and lower limits. That is,

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The sum of the values in the last column gives us ∑ f i x i . So, the mean of the given data is given by This new method of finding the mean is known as the Direct Method.

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So, from table, the mean of the deviations, Now, let us find the relation between and Since in obtaining di , we subtracted ‘a’ from each x i , so, in order to get the mean we need to add ‘ a ’ to .

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This can be explained mathematically as:

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The method discussed above is called the Assumed Mean Method .

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In assumed mean method example you have seen that when we found out di which are divisible by the size of class interval(h).If we divide di by h then we get ui. u i = d i /h =x i -a/h Then,we multiple the frequencies with their respective ui.Hence we get ∑f i u i .

Here a=70 and h=10:

Literacy rate(%) No. Of cities(fi) xi di= xi -70 ui = di/10 fiui 45-55 3 50 -20 -2 -6 55-65 10 60 -10 -1 -10 65-75 1 1 70 0 0 0 75-85 8 80 10 1 8 85-95 3 90 20 2 6 TOTAL 35 -2 Literacy rate(%) 45-55 55-65 65-75 75-85 85-95 No. of cities(fi) 3 10 11 8 3 Here a=70 and h=10 This method of finding mean is called Step Deviation Method .

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THANK YOU  JASNA NASEER L CLASS: X B

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