In this post, we will share NCERT Class 10th Maths Book Solutions Chapter 14 Statistics Ex 14.4. These solutions are based on new NCERT Syllabus.

## NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.4

Question 1.

The following distribution gives the daily income of 50 workers of a factory.

Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.

Solution:

We have the cumulative frequency distribution as follows:

Now, we plot the points corresponding to the ordered pair (120, 12), (140, 26), (160, 34), (180, 40) and (200, 50) on a graph paper and join them by a free hand to get a smooth curve as shown below:

The curve so obtained is called the less than ogive.

Question 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.

Solution:

Here, the values 38, 40, 42, 44, 46, 48, 50 and 52 are the upper limits of the respective class-intervals.

We plot the points (ordered pairs) (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 to get a smooth curve.

The curve so obtained is the less than type ogive.

∵ N = 35

∴ \(\frac{N}{2}=\frac{35}{2}\) = 17.5

The point 17.5 is on y-axis.

From this point (i.e., from 17.5) we draw a line parallel to the x-axis which cuts the curve at P. From this point P, draw a perpendicular to the x-axis, meeting the x-axis at Question The point Q represents the median of the data which is 47.5.

Verification:

To verify the result, let us make the following table in order to find median using the formula :

Thus, the median = 46.5 kg is approximately

Question 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.

Solution:

For more than type distribution, we have

Now, we plot the points (50, 100), (55, 98), (60, 90), (65, 78), (70, 54) and (75, 16) and join the points with a free hand to get a smooth curve.

The curve so obtained is the ‘more than type ogive’.