Facts or figures, collected with a definite purpose, are called data. Statistics is the area of study dealing with the presentation, analysis and interpretation of data. How data can be presented graphically in the form of bar graphs, histograms and frequency polygons.
The three measures of central tendency for ungrouped data are: Mean, Median and Mode.
Mean: It is found by adding all the values of the observations and dividing it by the total number of observations.
Median: It is the value of the middle-most observations.
Mode: The mode is the most frequently occurring observation.
Class 10
In this chapter, you will study how to measure mean, median and mode of grouped data. You will also learn the concept of cumulative frequency, the cumulative frequency distribution and how to draw cumulative frequency curves, called ogives.
The mean for grouped data can be found by:
- direct method
- assumed mean method
- step deviation method
with the assumption that the frequency of a class is centred at its mid-point, called its class mark.
The cumulative frequency of a class is the frequency obtained by adding the frequencies of all the classes preceding the given class.
Representing a cumulative frequency distribution graphically as a cumulative frequency curve, or an ogive of the less than type and of the more than type. The median of grouped data can be obtained graphically as the x-coordinate of the point of intersection of the two ogives for this data.