statistics

STATISTICS : 

STATISTICS GRAPHICAL REPRESENTATION

HISTOGRAM : 

HISTOGRAM A histogram is a two dimensional graphical representation of continuous frequency distribution. In a histogram rectangles are drawn with bases proportional to class intervals and heights proportional to the frequencies of respective classes.

Slide 3: 

To draw a histogram (1) Mark class intervals on X-axis and frequencies on Y-axis. (2) The scales for both the axes need not be the same. (3) Class intervals must be exclusive. If the intervals are in inclusive form, convert them to the exclusive form. (4) Draw rectangles with class intervals as bases and the corresponding frequencies as heights. The class limits are marked on the horizontal axis and the frequency is marked on the vertical axis. Thus a rectangle is constructed on each class interval.

Slide 4: 

Draw a histogram to represent the following.

Slide 5: 

In the above example, the intervals are exclusive. Now, let us consider an example with inclusive intervals. The daily wages of 50 workers, in rupees, are given below: In table (a), the class intervals are inclusive. So we convert them to the exclusive form as shown in table (b). Table (a) Table(a)

Slide 6: 

able (b)

Slide 7: 

(i) The class intervals are made continuous and then the histogram is constructed. (ii) A kink or a zig - zag curve is shown near the origin. It indicates that the scale along the horizontal axis does not start at the origin. (iii) The horizontal scale and vertical scale need not be the same.

Slide 8: 

Frequency polygon is a closed figure got by joining the Middle points of the top of rectangles of histograms. The extremes are joined with X-axis at a distance of half the length of class-interval from the extremes of the variable of the class-interval. It can be constructed by taking middle points of class intervals on X-axis and the frequency on Y-axis. These points are joined. Two extremes are joined with base in such a way that they touch the X-axis at half the distance of class interval outside the extreme points. If we have to construct histogram and frequency polygon both, then we have to join the mid points of the tops of all the rectangles and finally two extreme points with the points outside the extreme rectangles. FREQUENCY POLYGON

Slide 9: 

The weights of 50 students are recorded below. Draw a frequency polygon for this data. Draw a frequency polygon for the following

Slide 10: 

Draw a histogram and frequency polygon on the same graph paper giving the age of doctors working in a city