Descriptive statistics

Descriptive statistics generally show basic data, such as frequencies, means, mode, median to summarize the findings. Moreover, it shows the dispersion/ range of data by using minimum, maximum, range, variance and standard deviation (Allen.P, Bennett.K, 2012). The result of descriptive statistics will be portraying in charts.

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 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 grouped data. We shall also discuss the concept of cumulative frequency, the cumulative frequency distribution and how to draw cumulative frequency curves, called ogives. 14.2 Mean of Grouped Data 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 x = 1 1 2 2 1 2 + + + + + +

2012

Statistics has two major chapters • Descriptive Statistics • Inferential statistics Descriptive Statistics. It provides mathematical and graphic procedures to summarize the information of the data in a clear and understandable way. The tools in descriptive statistics are graphical presentations and mathematical formulas. Inferential Statistics. It provides procedures to draw inferences (to say something) about a population from results obtained from a subset of the units in the population (sample). In order to give some measure of the reliability of those inferences, statistics uses probability concepts.

Statistics is concerned with scientific methods for collecting, organizing, summarizing, Presenting and analyzing data as well as deriving valid conclusions and making reasonable Decisions on the basis of this analysis. Statistics is concerned with the systematic collection of Numerical data and its interpretation.