Cumulative Frequency Distribution of Less Than Type

Q.

How to find missing frequency in median
For example:
If the median of the distribution given below is 46, find the value of the missing frequencies.

class interval	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Frequency	12	30	$f_1$	65	$f_2$	25	18

Q. Question 7
The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
$\begin{array}{cccccccc}Weight\left(inkg\right)& 40-45& 45-50& 50-55& 55-60& 60-65& 65-70& 70-75\\ Numberofstudents& 2& 3& 8& 6& 6& 3& 2\end{array}$

Q.

The following table gives the life-time (in days) of 100 electric bulbs of a certain brand.

$\begin{array}{ccccccc}Life-time\left(indays\right)& Lessthan50& Lessthan100& Lessthan150& Lessthan200& Lessthan250& Lessthan300\\ Numberofbulbs& 7& 21& 52& 79& 91& 100\end{array}$

From this table, construct the frequency distribution table.

Q.

Which of the given less than cumulative frequency curve (ogive) correctly represents the following distribution?

$\begin{array}{cccccc}\text{Height}& 110-120& 120-130& 130-140& 140-150& 150-160\\ \text{Number of students}& 7& 9& 12& 10& 4\end{array}$

1. 

2. 

3. 

4. 

Q. Find the value of p for the following distribution whose mean is 16.6.

x:	8	12	15	p	20	25	30
f:	12	16	20	24	16	8	4

Q.

The following table shows the distribution of the daily wages earned by workers in a building site.

Wages (in Rs/day)	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$	$100-110$	$110-120$	$120-130$
No. of workers	$12$	$20$	$30$	$38$	$24$	$16$	$12$	$8$

Change the distribution to a more than type distribution and draw its ogive. Hence, obtain the median wage per day from the graph.

Q.

The following table shows the distribution of the heights of a group of factory workers :

$\begin{array}{cccccccc}\text{Ht. (cm):}& 150-155& 155-160& 160-165& 165-170& 170-175& 175-180& 180-185\\ \text{No. of workers}& 6& 12& 18& 20& 13& 8& 6\end{array}$

(i) Determine the cumulative frequencies.

(ii) Draw the 'less than' cumulative frequency curve on graph paper. Use 2 cm = 5 cm height on one axis and 2 cm = 10workers on the other.

Q.

The frequency distribution table below shows the marks of students. Find the number of people who obtained marks less than 22.5.

$$\begin{array}{cccccc}Class& 12.5-17.5& 17.5-22.5& 22.5-27.5& 27.5-32.5& 32.5-37.5\\ Frequency& 2& 22& 19& 14& 13\end{array}$$

1. 21

2. 22

3. 23

4. 24

Q.

(a) Use the information given in the adjoining histogram to construct a frequency table.

(b) Use this table to construct an ogive

Q.

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

Production yield (in kg/ha)	50 − 55	55 − 60	60 − 65	65 − 70	70 − 75	75 − 80
Number of farms	2	8	12	24	38	16

Change the distribution to a more than type distribution and draw ogive.

Q. Question 7
Consider the following frequency distribution
$\begin{array}{cccccc}Class& 0.5& 6-11& 12-17& 18-23& 24-29\\ Frequency& 13& 10& 15& 8& 11\end{array}$
The upper limit of the median class is
(a) 17
(b) 17.5
(c) 18
(d) 18.5

Q.

Which of the following are the possible ages of ${27}^{th}$ and ${32}^{nd}$ observations in the given grouped distribution in increasing order of age? All the persons (observations) part of the distribution have exact integral ages.

$$\begin{array}{cc}Agelessthan& Numberofpeople\\ 15& 3\\ 16& 11\\ 17& 21\\ 18& 31\\ 19& 36\\ 20& 40\end{array}$$

1. 15, 16
2. 17, 18
3. 18, 19
4. 14, 15

Q.

Question 5
The following table gives the distribution of the life time of 400 neon lamps:

$\begin{array}{cc}Lifetime\left(inhours\right)& Numberoflamps\\ 1500-2000& 14\\ 2000-2500& 56\\ 2500-3000& 60\\ 3000-3500& 86\\ 3500-4000& 74\\ 4000-4500& 62\\ 4500-5000& 48\end{array}$

Find the median life time of a lamp.

Q. Draw a less than ogive for the following frequency distribution

Marks	No. of students
0 - 4	8
4 - 8	4
8 - 12	6
12 - 16	12
16 - 20	10

1. (4, 6) (6 , 10) (12, 22) (18, 28) (20, 32)
2. (4, 10) (8, 10) (12, 20) (18, 28) (20, 32)
3. (4, 8) (8, 12) (12, 18) (16, 30) (20, 40)
4. (6, 4) (8, 10) (12, 20) (18, 26) (22, 32)

Q.

Find the median for the following data

$$\begin{array}{ccccccc}Classinterval& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ Frequency& 16& 20& 32& 48& 30& 14\end{array}$$

Q.

Find the Median for the given data by drawing a 'less than ogive' :

$\begin{array}{cccccc}\text{Class Interval}& 0-10& 10-20& 20-30& 30-40& 40-50\\ \text{Frequency}& 5& 10& 14& 16& 8\end{array}$

1. 35

2. 28

3. 29

4. 31

Q. The table below gives the volume of water (in litres) Suzanne drank in the last 40 days. Find the median of this data.
$$\begin{array}{cc}Volume& Number\\ ofwater\left(l\right)& ofdays\\ 1-2& 6\\ 2-3& 8\\ 3-4& 12\\ 4-5& 6\\ 5-6& 8\end{array}$$

1. 2
2. 4
3. 3.5
4. 5.5

Q. The following table gives the production yield per hectare of wheat of 100 farms of a village.

Production yield in kg/hectare	50-55	55-60	60-65	65-70	70-75	75-80
Number of frames	2	8	12	24	38	16

Change the above distribution to more than type distribution and draw its ogive.

Q. Draw a histogram and frequency polygon for the following frequency distribution.

Class	5-10	10-15	15-20	20-25	25-30
Frequency	20	30	50	40	10

Q.

Find the median of the following data.

$$\begin{array}{cccccc}Classinterval& 0-10& 10-20& 20-30& 30-40& 40-50\\ Frequency& 8& 10& 14& 10& 8\end{array}$$

Q. Find the missing value of p for the following distribution whose mean is 12.58

x:	5	8	10	12	p	20	25
f:	2	5	8	22	7	4	2

Q.

In a survey of 200 students from 7 different schools, 50 people do not play only NFS, 40 people do not play only Dota and 10 people play no online games. Then find the no. of people out of 200 people who do not play both the games.

1. {3}

2. {1, 2, 3, 4}

3. {1, 2, 4, 5}

4. {1, 2, 3, 4, 5, 6}

Q.

Find the median of the following cumulative frequency distribution:
$\begin{array}{ccc}\text{x}& \text{frequency}& \text{Cumulative frequency}\\ 22& 1& 1\\ 34& 2& 3\\ 39& 2& 5\\ 45& 8& 13\\ 54& 8& 21\\ 56& 9& 30\\ 68& 4& 34\\ 78& 4& 38\\ 84& 2& 40\end{array}$

1. 49.5

2. 53.5

3. 54

4. 55

Q. Following is the distribution of marks of 70 students in a periodical test:

Marks	Number of students
Marks less than 10 Marks less than 20 Marks less than 30 Marks less than 40 Marks less than 50	3 11 28 48 70

Draw a cumulative frequency curve for the above data and find the median.

Q.

$$\begin{array}{cccccc}Weeklywages(inRs.)& 0-100& 100-200& 200-300& 300-400& 400-500\\ Numberofworkers& 40& 39& 34& 30& 45\end{array}$$

What is the number of people whose wage is less than Rs.400?

1. 40

2. 79

3. 139

4. 143

Q.

The monthly income of a group of 320 employees in a company is as follows :

Monthly income (in Rs.1000) 6 – 7 7 – 8 8 – 9 9 – 10 10 – 11 11 – 12 12 – 13

Number of employees 20 45 65 95 60 30 5

Draw an ogive for the given distribution taking 2cm = Rs.1000 on one axis & 2cm = 50 employees on the other axis. Using the graph determine:

1. 930, 20, 25000

2. 800, 20, 20000

3. 930, 10, 15000

4. 930, 15, 10250

5. 800, 10, 20000

6. 800, 15, 10250

7. 800, 20, 15100

Q. Which measure of central tendency is obtained graphically as the x coordinate of the point of intersection of the two ogives?
(a) Mean
(b) Median
(c) Mode
(d) None of these

Q. The median of a given frequency distribution is found graphically with the help of __________.

1. Frequency polygon
2. Histogram
3. Frequency curve
4. Ogive

Q. The abscissa of intersection of 'less than' type ogive and 'more than' type ogive is:

1. Mean
2. Median
3. Mode
4. All of these

Q.

The following table has been given with the relevant class mark and frequency.

$\begin{array}{cc}\text{Class mark}& \text{Frequency}\\ 5& 8\\ 15& 10\\ 25& 2\\ 35& 4\\ 45& 7\\ 55& 3\end{array}$

Draw a Histogram for the given distribution.