# RD SHARMA Solutions for Class 10 Mathematics Chapter 7: Statistics

This chapter extends the topics studied in class 9 where students learnt how to classify a given ungrouped data and their numerical representatives, better known as the measures of central tendency. The three broad classifications of the measures of central tendency are mean, median and mode. Thus, chapter 7-Statistics deals with the study of the measures of central tendency for grouped data.

This chapter initiates with a brief introduction of the mean for grouped data. The mean of a given data is the sum of all the observations divided by the total number of observations made. It is represented by:

Mean = (f1x1+ f2x2+…..fnxn) ÷ (f1+f2+…..fn)

It also introduces two methods for calculating the mean for a given grouped data: the Assumed Mean Method and the Step-Deviation Method. These methods are great to use when the data provided is in well-defined groups and comprises class intervals.

Chapter 7: Statistics then talks about the calculation of Mode for a grouped data. As we recall from Class 9, the Mode of a given data is that value that occurs the maximum number of times. Thus, precisely speaking, the mode of data is the value that has the maximum frequency of occurrence.

The chapter then concludes with the methods to calculate the Median of a grouped data. A new method for the purpose mentioned above has been elaborated, namely the cumulative frequency method. A specific formula that exhibits the relationship between the mean, median and the mode of a given data is also mentioned in this chapter. This is known as the Empirical formula.

3 Median = Mode + 2 Mean