KC Sinha: Exercise 6.4 – Mathematics Solution Class 10 Chapter 6 Statistics

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.

Sol :

Now, taking upper class limits on x- axis and their respective frequencies on y-axis we can draw its ogive as follows:

Question 2 

Draw ‘more than’ ogive of the following distribution:

Sol :

Now, taking lower class limits on x- axis and their respective frequencies on y-axis we can draw its ogive as follows:

Question 3 

Draw a less than type cumulative frequency curve for the following data and from the graph find the median:

Sol :

Now, taking upper class limits on x- axis and their respective frequencies on y-axis we can draw its ogive as follows:

Now, we have n = 250

The cumulative Frequency just greater than  is 140 then the median class is 300-400 such that
the lower limit (l) = 300
cumulative frequency of the class preceding 300-400 (cf) = 75
frequency of the median class 300-400 = 65,
class size (h) = 100
Using the formula,Median =1+n2−cff×h,we have

Median =300+125−7565×100
= 300 +76.9
= 376.9
=377 (approx.)

Question 4 

Convert the following distribution into ‘more than’ frequency distribution and draw more than’ ogive. Also find the median from it.

Sol :

Now, taking lower class limits on x-axis and their respective frequencies on y-axis we can draw its ogive as follows:

Now, we have n = 201
⇒n2=2012=100.5
The cumulative Frequency just greater than n2 is 156 then the median class is 40 – 60 such that
the lower limit (l) = 40
cumulative frequency of the class preceding 40 – 60 (cf) = 92
frequency of the median class 40-60 = 64,
class size (h) = 20
Using the formula, Median =1+n2−cff×h, we have

Median =40+100.5−9264×20
= 40 +2.65
= 42.65
= 42.7

Question 5

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

Draw both ogives for the data given above and hence obtain the median profit.
Sol :

Now, taking upper-class limits on x-axis and their respective frequencies on y-axis we can draw its ogive as follows:

Now, we have n = 30
⇒n2=302=15
The cumulative Frequency just greater than n2 is 16 then the median class is 15 – 20 such that
the lower limit (l) = 15
cumulative frequency of the class preceding 15 – 20 (cf) = 14
the frequency of the median class 15 – 20 = 2,
class size (h) = 5

Using the formula, Median =1+n2−cff×h, we have

Median =15+15−142×5
= 15 + 2.5
= 17.5
So, the median profit is Rs. 17.5

Question 6

The following table gives the distribution of the monthly income of 600 families in a certain city:

Draw a ‘less than’ and ‘more than’ ogive curve for the above data on the same graph and from these find the median.
Sol :

Now, taking monthly income on x-axis and their respective frequencies on y-axis we can draw its ogive as follows:

Now, we have n = 600
⇒n2=6002=300
The cumulative Frequency just greater than n2 is 430 then the median class is 150 – 225 such that
the lower limit (l) = 150
cumulative frequency of the class preceding 150 – 225 (cf) = 230
frequency of the median class 150 – 225 = 200,
class size (h) = 75

Using the formula,Median =1+n2−cff×h,we have

Median =150+300−230200×75
=150+70200×75
= 150 +26.25
= 176.25
= 176(approx.)