Ogive of Less Than Type

Q.

Find the mean, mode and median of the following frequency distribution. [CBSE 2010]

Class	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	4	4	7	10	12	8	5

Q.

The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.

Monthly consumption (in units)	Number of consumers
65 − 85	4
85 − 105	5
105 − 125	13
125 − 145	20
145 − 165	14
165 − 185	8
185 − 205	4

Q.

Draw less than ogive and more than ogive on a single graph paper and hence find the median of the following data:

Class interval	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Frequency	2	12	2	4	3	4	3

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

Production yield in kg per hectare:	50−55	55−60	60−65	65−70	70−75	75−80
Number of farms:	2	8	12	24	38	16

Draw less than ogive and more than ogive.

Q. In the following data, find the values of p and q. Also, find the median class and modal class.

Class	Frequency (f)	Cumulative frequency (cf)
100−200	11	11
200−300	12	p
300−400	10	33
400−500	q	46
500−600	20	66
600−700	14	80

Q. The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.

Monthly consumption: (in units)	65−85	85−105	105−125	125−145	145−165	165−185	185−205
No. of consumers:	4	5	13	20	14	8	4

Q.

If length , breadth and height of cuboid are increased by 20 %, what is the percentage increase in the the total surface area of cuboid?

Q.

If the 'less than type' ogive and 'more than type' ogive intersect each other at (20.5, 15.5) then the median of the given data is

(a) 5.5 (b) 15.5 (c) 20.5 (d) 36.0

Q.

Marks obtained by 200 students in an examination are given below :

Draw an ogive for the given distribution taking 2cm = 10 marks on one axis & 2 cm = 20 students on the other axis. Using the graph determine:

1. 57, 30, 15

2. 57, 46, 10

3. 57, 25, 20

4. 47, 30, 15

5. 47, 25, 20

6. 47, 46, 10

Q. ​​The following table gives the frequency distribution of the percentage of marks obtained by 2300 students in a competitive examination.

Marks obtained (in per cent)	11−20	21−30	31−40	41−50	51−60	61−70	71−80
Number of students	141	221	439	529	495	322	153

(a) Convert the given frequency distribution into the continuous form.

(b) Find the median class and write its class mark.

(c) Find the modal class and write its cumulative frequency.

Q. In a class test, 50 students obtained marks as follows:

Marks obtained	0−20	20−40	40−60	60−80	80−100
Number of students	4	6	25	10	5

Find the modal class and the median class. [CBSE 2014]

Q.

If the median of the distribution is given below is 28.5, find the values of x and y.

Class interval	Frequency
0 − 10	5
10 − 20	x
20 − 30	20
30 − 40	15
40 − 50	y
50 − 60	5
Total	60

Q.

The below question consists of problem figures and followed by four answer figures (A), (B), (C) and (D). Find out the figure from the answer figures which will continue the given series.

1. B

2. C

3. D

4. A

Q.

Find the median of the following data by making a 'less than ogive'.

$\begin{array}{ccccccccccc}Marks& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70& 70-80& 80-90& 90-100\\ Numberofstudents& 5& 3& 4& 3& 3& 4& 7& 9& 7& 8\end{array}$

Q. The following table gives the daily income of 50 workers of a factory :

Daily income (in ₹) 100-120 120-140 140-160 160-180 180-200

Number of workers : 12 14 8 6 10

Find the mean, mode and median of the above data .

Q.

The distribution of heights (in cm) of 96 children is given below. Construct a histogram and a frequency polygon on the same axes.

$\begin{array}{ccccccccccc}\text{Height(in cm)}& 124& 128& 132& 136& 140& 144& 148& 152& 156& 160\\ & to& to& to& to& to& to& to& to& to& to\\ & 128& 132& 136& 140& 144& 148& 152& 156& 160& 164\\ \text{No. of Children}& 5& 8& 17& 24& 16& 12& 6& 4& 3& 1\end{array}$

Q.

If the point of intersection of a less than and more than ogive is (15, 20), then the value of median is

1. 20

2. 5

3. 15

4. 35

Q.

Draw an ogive for each of the following distributions :

(i) $\begin{array}{cccccc}Marksobtained& lessthan10& lessthan20& lessthan30& lessthan40& lessthan50\\ Frequency& 8& 25& 38& 50& 67\end{array}$

(ii) $\begin{array}{cccccccc}\text{Age in years (less than)}& 10& 20& 30& 40& 50& 60& 70\\ \text{Frequency}& 0& 17& 32& 37& 53& 58& 65\end{array}$

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

Production yield (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 its ogive. Using ogive, find the median of the given data. [CBSE 2013]

Q.

The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition.

$\begin{array}{cc}\text{Scores}& \text{No. of shooters}\\ 0-10& 10\\ 10-20& 12\\ 20-30& 15\\ 30-40& 8\\ 40-50& 20\\ 50-60& 24\\ 60-70& 7\\ 70-80& 11\\ 80-90& 30\\ 90-100& 18\end{array}$

Use a graph sheet to draw an ogive for the distribution.

Estimate the number of shooters who obtained a score of more than 85%.

1. 40
2. 28
3. 34
4. 37

Q.

The given distribution shows the number of wickets taken by the bowlers in one-day international cricket matches:

$\begin{array}{ccccccccc}Numberofwickets& Lessthan15& Lessthan30& Lessthan45& Lessthan60& Lessthan75& Lessthan90& Lessthan105& Lessthan120\\ Numberofbowlers& 2& 5& 9& 17& 39& 54& 70& 80\end{array}$

Draw a 'less than type' ogive from the above data.Find the median.

Q. For a symmetrical frequency distribution, we have:
(a) mean < mode < median
(b) mean > mode > median
(c) mean = mode = median
(d) mode = $\frac{1}{2}$ (mean + median)

Q. Draw a " less than type " ogive and "more than type" ogive for the following distribution and hence obtain the median from the graph

C.I.	20 - 30	30-40	40-50	50-60	60-70	70-80	80-90
Frequency	8	12	24	6	10	15	25

Q. For a given data with 70 observations the less then ogive and the more than ogive intersect at (20.5, 35). The median of the data is

(a) 20

(b) 35

(c) 70

(d) 20.5

Q. The following table shows the ages of 100 persons of a locality.

Age (yrs)	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Number of persons	5	15	20	23	17	11	9

Represent the above as the less than type frequency distribution and draw an ogive for the same.

Q.

From the ogive curve, answer the following question.

How many students secured marks between 50% and 70% ?

___

Q.

Median of a given frequency distribution is found with the help of a

1. Bar graph

2. Ogive

3. Histogram

4. Pie Chart

Q. If the median of the following frequency distribution is 32.5, find the values of f₁ and f₂.

Class interval	0-10	10-20	20-30	30-40	40-50	50-60	60-70	Total
Frequency	f1	5	9	12	f2	3	2	40

Q.

The less than ogive is a rising graph.

1. True

2. False

Q.

From the given ogive, which of the following can be determined?

1. Mean only

2. Median only

3. Mode only

4. Mean, median and mode