Chapter 7: Statistics Exercise – 7.6

Question: 1

Draw an Ogive by less than the method for the following data:

Solution:

We need to plot the points (1, 4), (2, 3), (3, 35), (4, 63), (5, 87), (6, 99), (7, 107), (8, 113), (9, 118), (10, 120), by taking upper class limit over the x-axis and cumulative frequency over the y-axis.

Question: 2

The marks scored by 750 students in an examination are given in the form of a frequency distribution table:

Solution:

Plot the points (640, 16), (680, 61), (720, 217), (760, 501), (800, 673), (840, 732), (880, 750) by taking upper class limit over the x-axis and cumulative frequency over the y-axis.

Question: 3

Draw an Ogive to represent the following frequency distribution:

Solution:

The given frequency distribution is not continuous, so we will first make it continuous and then prepare the cumulative frequency: 

Plot the points (4.5, 2), (9.5, 8), (14.5, 18), (19.5, 23), (24.5,26) by taking the upper class limit over the x-axis and cumulative frequency over the y-axis.

Question: 4

The monthly profits (in Rs) of 100 shops are distributed as follows:

Draw the frequency polygon for it 

Solution:

We have

Question: 5

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

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

Solution:

We first prepare the cumulative frequency table by less than method as given below:

Now we mark on x-axis upper class limit, y-axis cumulative frequencies. Thus we plot the point (120, 12), (140, 26), (160, 34), (180, 40), (200, 50).

Question: 6

The following table gives production yield per hectare of wheat of 100 farms of a village:

Draw 'less than' ogive and 'more than' ogive

Solution:

Less than method: Cumulative frequency table by less than method

Now we mark on x-axis upper class limit, y-axis cumulative frequencies. We plot the point (50,100), (55, 98), (60, 90), (65, 78), (70, 54), (75, 16)

Question: 7

During the medical check-up of 35 students of a class, their weight recorded as follows:

Draw a less than type ogive for the given data. Hence, obtain the median weight from the graph and verify the verify the result my using the formula.

Solution:

Less than method: It is given that On x-axis upper class limits. Y-axis cumulative frequency We plot the points (38, 0), (40, 3), (42, 5), (44, 9), (46, 4), (48, 28), (50, 32), (52, 35).

More than method: cumulative frequency

x – axis lower class limits on y-axis cf We plot the points (38, 35), (40, 32), (42, 30), (44, 26), (46, 26), (48, 7), (50,3).

Question: 8

The following table shows the height of trees:

Draw 'less than' ogive and 'more than' ogive

Solution:

By less than method

Plot the points (7, 26), (14, 57), (21, 92), (28, 134), (35, 216), (42, 287), (49, 341), (56, 360) by taking upper class limit over the x-axis and cumulative frequency over the y-axis.

By more than method:

Question: 9

The annual profits earned by 30 shops of a shopping complex in a locality give rise to the following distribution:

Draw both ogive for the above data and hence obtain the median.

Solution:

More than method:

Now, we mark on x-axis lower class limits, y-axis cumulative frequency. Thus, we plot the points (5, 30), (10, 28), (15, 16), (20, 14), (25,10), (30, 7) and (35, 3)

Less than method:

Now we mark the upper class limits along x-axis and cumulative frequency along y-axis. Thus we plot the points (10, 2), (15,14), (20,16), (25, 20), (30, 23), (35, 27), (40, 30).

We find that the two types of curves intersect of P from point L it is drawn on x-axis The value of a profit corresponding to M is 17.5. Hence median is 17.5 lakh