# statistics for class 10

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Information about statistics for class 10
Education

Published on July 17, 2012

Author: jashank

Source: authorstream.com

PowerPoint Presentation: In Class IX, you have studied the classification of given data into 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 (including those of varying widths) and frequency polygons. In fact, you went a step further by studying certain numerical repr esentatives of the ungroup ed 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 grouped data . We shall also discuss the concept of cumulativ e frequency, the cumulative frequency distribution and how to draw cumulative frequency curves, called ogives . PowerPoint Presentation: 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 f requencies 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 o f the values of all the observations = f 1 x 1 + f 2 x 2 + . . . + fnxn , and the number of observations = f 1 + f 2 + . . . + fn . So, the mean x of the data is given by Recall that we can write this in short form by using the Greek letter Σ (capital sigma) which means summation. That is, PowerPoint Presentation: The marks obtained by 30 students of Class X of a certain school in a Mathematics paper consisting of 100 mark s are presented in table below. Find the mean of the marks obtained by the students. PowerPoint Presentation: 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 classinterval 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 class mark) by finding the average of its upper and lower limits. That is, PowerPoint Presentation: The sum of the values in the last column gives us Σ fi xi . So, the mean x of the given data is given by This new method of finding the mean is known as the Direct Method . PowerPoint Presentation: So, from Table 14.4, the mean of the deviations, Now, let us find the relation between d and x . Since in obtaining di , we subtracted ‘a’ from each xi , so, in order to get the mean x , we need to add ‘ a ’ to d . This can be explained mathematically as: PowerPoint Presentation: The method discussed above is called the Assumed Mean Method .

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