In NCERT Solution For Class 10, Maths, Chapter 14, Statistics, Exercise 14.4, we will discuss Graphical Representation of Cumulative Frequency Distribution. 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. and 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.
Class 10, Maths, Chapter 14, Exercise 14.4 Solutions
Q.1. The following table gives production yield per hectare of wheat of 100 farms of a village.
Change the distribution to a more than type distribution, and draw its ogive
Ans: Converting the given distribution to a less than type cumulative frequency distribution, we get
Let us now plot the points corresponding to the ordered pairs (120,12), (140,26), (160,34), (180, 40 ) and (200, 50) on a graph paper and join them by a free hand smooth curve
The curve thus obtained is called the less than ogive
Q.2. During the medical check-up of 35 students of a class, their weights were recorded as
follows:
Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.
Ans: Here the values 38, 40, 42, 44, 46, 48, 50 and 52 are the upper limits of the respective class-intervals.
Let us now plot the points corresponding to the ordered pairs given by (38, 0), (40, 3), (42,5), ( 44,9 ), ( 46,14), ( 48,28), (50,32) and (52,35) on a graph paper and join them by a free hand smooth curve
The curve thus obtained is the less than type ogive.
To locate $\frac{n}{2}=\frac{35}{2}$ = 17.5 on the y-axis. From this point, we draw a line parallel to x-axis cutting the curve at a point. From this point draw a perpendicular to the a- line parallel to the x-axis. The point of intersection of this perpendicular with the x-axis gives the median of the data. In this case it is 46.95
Let us make the following table in order to find mode by using the formula
Q.3. The following table gives production yield per hectare of wheat of 100 farms of a village.
Change the distribution to a more than type distribution, and draw its ogive
Ans:
Converting the given distribution to a more than type distribution, we get
Now, we draw the ogive by plotting the points (50, 100), (55, 98), (60,90), (65,78), (70, 54) and (75, 16) on the graph paper.
curve thus obtained is more than type ogive.