Ex-7.6 Statistics, Class 10, Maths RD Sharma Solutions | Extra Documents, Videos & Tests for Class 10 PDF Download

Q.1 Draw an ogive by less than the method for the following data:

Sol :

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.

Q.2): The marks scored by 750 students in an examination are given in the form of a frequency distribution table:

Sol :

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.

Q.3) Draw an ogive to represent the following frequency distribution:

Sol :

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.

Q.4) The monthly profits (in Rs) of 100 shops are distributed as follows:

Draw the frequency polygon for it

Sol :

We have

Q.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.

Sol :

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).

Q.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

Sol :

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)

Q.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.

Sol : 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)

We find the two types of curves intersect at a point P. From point P perpendicular PM is draw on x-axis

The verification,

We have

Now, N = 35

N2=17.5

The cumulative frequency just greater than N2 is 28 and the corresponding class is 46 – 48

Thus 46 – 48 is the median class such that

L = 46, f = 14, C1=14 h = 2

Median = 

= 46 +7/14

46.5

Median = 46.5 kg

Hence verified

Q.9) The following table shows the height of trees:

Draw ‘less than ‘ogive and ‘more than ‘ogive

Sol :

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:

Take lower class limit over the x-axis and CF over the y-axis and plot (0,360) , (7,334) , (14,303) , (21,268)  (28,226) , (35,144) , (42,73) , (49,19).

Q.10) 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.

Sol :

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