| 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 |
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 thatthe 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.)
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
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
= 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
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
= 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.)
$=150+\frac{70}{200} \times 75$
= 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 |
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