KC Sinha Mathematics Solution Class 10 Chapter 6 Statistics Exercise 6.4

Exercise 6.1
Exercise 6.2
Exercise 6.3
Exercise 6.4

Exercise 6.4

Question 1

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

Daily income (in Rs)	100-120	120-140	140-160	160-180	180-200
Number of workers	12	14	8	6	10

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 $=1+\frac{\frac{n}{2}-c f}{f} \times h$,we have

Median $=300+\frac{125-75}{65} \times 100$
= 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
$\Rightarrow \frac{\mathrm{n}}{2}=\frac{201}{2}=100.5$
The cumulative Frequency just greater than $\frac{n}{2}$ 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 $=1+\frac{\frac{n}{2}-c f}{f} \times h$, we have

Median $=40+\frac{100.5-92}{64} \times 20$
= 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
$\Rightarrow \frac{\mathrm{n}}{2}=\frac{30}{2}=15$
The cumulative Frequency just greater than $\frac{n}{2}$ 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 $=1+\frac{\frac{n}{2}-c f}{f} \times h$, we have

Median $=15+\frac{15-14}{2} \times 5$
= 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
$\Rightarrow \frac{\mathrm{n}}{2}=\frac{600}{2}=300$
The cumulative Frequency just greater than $\frac{n}{2}$ 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 $=1+\frac{\frac{n}{2}-c f}{f} \times h$,we have

Median $=150+\frac{300-230}{200} \times 75$
$=150+\frac{70}{200} \times 75$
= 150 +26.25
= 176.25
= 176(approx.)

S.no	Chapters	Links
1	Real numbers	Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4
2	Polynomials	Exercise 2.1 Exercise 2.2 Exercise 2.3
3	Pairs of Linear Equations in Two Variables	Exercise 3.1 Exercise 3.2 Exercise 3.3 Exercise 3.4 Exercise 3.5
4	Trigonometric Ratios and Identities	Exercise 4.1 Exercise 4.2 Exercise 4.3 Exercise 4.4
5	Triangles	Exercise 5.1 Exercise 5.2 Exercise 5.3 Exercise 5.4 Exercise 5.5
6	Statistics	Exercise 6.1 Exercise 6.2 Exercise 6.3 Exercise 6.4
7	Quadratic Equations	Exercise 7.1 Exercise 7.2 Exercise 7.3 Exercise 7.4 Exercise 7.5
8	Arithmetic Progressions (AP)	Exercise 8.1 Exercise 8.2 Exercise 8.3 Exercise 8.4
9	Some Applications of Trigonometry: Height and Distances	Exercise 9.1
10	Coordinates Geometry	Exercise 10.1 Exercise 10.2 Exercise 10.3 Exercise 10.4
11	Circles	Exercise 11.1 Exercise 11.2
12	Constructions	Exercise 12.1
13	Area related to Circles	Exercise 13.1
14	Surface Area and Volumes	Exercise 14.1 Exercise 14.2 Exercise 14.3 Exercise 14.4
15	Probability	Exercise 15.1