RD Sharma Class 10 Ex 7.6 Solutions Chapter 7 Statistics

In this chapter, we provide RD Sharma Class 10 Ex 7.6 Solutions Chapter 7 Statistics for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Class 10 Ex 7.6 Solutions Chapter 7 Statistics pdf, Now you will get step by step solution to each question.

TextbookNCERT
ClassClass 10
SubjectMaths
ChapterChapter 7
Chapter NameStatistics
Exercise7.6
CategoryRD Sharma Solutions

RD Sharma Solutions for Class 10 Chapter 7 Statistics Ex 7.6 Download PDF

Chapter 7: Statistics Exercise – 7.6

 

Question: 1

Draw an Ogive by less than the method for the following data:

No. of roomsNo. of houses
14
29
322
428
524
612
78
86
95
102

Solution:

No. of roomsNo. of housesCumulative Frequency
Less than or equal to 1 44
Less than or equal to 2913
Less than or equal to 32235
Less than or equal to 42863
Less than or equal to 52487
Less than or equal to 61297
Less than or equal to 78107
Less than or equal to 86113
Less than or equal to 95119
Less than or equal to 102120

We need to plot the points (1, 4), (2, 3), (3, 35), (4, 63), (5, 87), (6, 99), (7, 107), (8, 113), (9, 118), (10, 120), by taking upper class limit over the x-axis and cumulative frequency over the y-axis.

Graph of Ogive

Question: 2

The marks scored by 750 students in an examination are given in the form of a frequency distribution table:

MarksNo. of Students
600 – 64016
640 – 68045
680 – 720156
720 – 760284
760 – 800172
800 – 84059
840 – 88018

Solution:

MarksNo. of StudentsMarks Less than Cumulative Frequency
600 – 6401664016
640 – 6804568061
680 – 720156720217
720 – 760284760501
760 – 800172800693
800 – 84059840732
840 – 88018880750

Plot the points (640, 16), (680, 61), (720, 217), (760, 501), (800, 673), (840, 732), (880, 750) by taking upper class limit over the x-axis and cumulative frequency over the y-axis.

Graph of Ogive

Question: 3

Draw an Ogive to represent the following frequency distribution:

Class-interval0 – 45 – 910 – 1415 – 1920 – 24
No. of students261053

Solution:

The given frequency distribution is not continuous, so we will first make it continuous and then prepare the cumulative frequency: 

Class-intervalNo. of StudentsLess thanCumulative frequency
0.5 – 4.524.52
4.5 – 9.569.58
9.5 – 14.51014.518
14.5 – 19.5519.523
19.5 – 24.5324.526

Plot the points (4.5, 2), (9.5, 8), (14.5, 18), (19.5, 23), (24.5,26) by taking the upper class limit over the x-axis and cumulative frequency over the y-axis.

Graph of Ogive

Question: 4

The monthly profits (in Rs) of 100 shops are distributed as follows:

Profit per shopNo of shops:
0 – 5012
50 – 10018
100 – 15027
150 – 20020
200 – 25017
250 – 3006

Draw the frequency polygon for it 

Solution:

We have

Profit per shopMid-value  No of shops:
Less than 000
Less than 0 – 602512
Less than 60 – 1207518
Less than 120 – 18012527
Less than 180 – 24017520
Less than 240 – 30022517
Less than 300 – 3602756
Above 3603000
Graph of Ogive

Question: 5

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

Daily income (in Rs):No of workers:
100 – 12012
120 – 14014
140 – 1608
160 – 1806
180 –  20010

Convert the above distribution to a ‘less than’ type cumulative frequency distribution and draw its ogive.

Solution:

We first prepare the cumulative frequency table by less than method as given below:

Daily incomeCumulative frequency
<12012
<14026
<16034
<18040
<20050

Now we mark on x-axis upper class limit, y-axis cumulative frequencies. Thus we plot the point (120, 12), (140, 26), (160, 34), (180, 40), (200, 50).

Graph of Ogive

Question: 6

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

Production yield:No of farms:
50 – 552
55 – 608
60 – 6512
65 – 7024
70 – 7538
75 – 8016

Draw ‘less than’ ogive and ‘more than’ ogive

Solution:

Less than method: Cumulative frequency table by less than method

Production yieldNumber of farmsProduction yield more thanCumulative frequency
50 – 552552
55 – 6086010
60 – 65126522
65 – 70247046
70 – 80387584
75 – 801680100

Now we mark on x-axis upper class limit, y-axis cumulative frequencies. We plot the point (50,100), (55, 98), (60, 90), (65, 78), (70, 54), (75, 16)

Graph of Ogive

Question: 7

During the medical check-up of 35 students of a class, their weight recorded as follows:

Weight (in kg)No of students
Less than 380
Less than 403
Less than 425
Less than 449
Less than 4614
Less than 4828
Less than 5032
Less than 5235

Draw a less than type ogive for the given data. Hence, obtain the median weight from the graph and verify the verify the result my using the formula.

Solution:

Less than method: It is given that On x-axis upper class limits. Y-axis cumulative frequency We plot the points (38, 0), (40, 3), (42, 5), (44, 9), (46, 4), (48, 28), (50, 32), (52, 35).

More than method: cumulative frequency

WeightNo. of studentsWeight more thanCumulative frequency
38 – 4033834
40 – 4224032
42 – 4444230
44 – 4654426
46 – 48144621
48 – 504487
50 – 523503

x – axis lower class limits on y-axis cf We plot the points (38, 35), (40, 32), (42, 30), (44, 26), (46, 26), (48, 7), (50,3).

Graph of Ogive

Question: 8

The following table shows the height of trees:

HeightNo. of trees
Less than  7 26
Less than  1427
Less than  2192
Less than  28134
Less than  35216
Less than  42287
Less than  49341
Less than  56360

Draw ‘less than’ ogive and ‘more than’ ogive

Solution:

By less than method

HeightNo. of trees
Less than  7 26
Less than  1427
Less than  2192
Less than  28134
Less than  35216
Less than  42287
Less than  49341
Less than  56360

Plot the points (7, 26), (14, 57), (21, 92), (28, 134), (35, 216), (42, 287), (49, 341), (56, 360) by taking upper class limit over the x-axis and cumulative frequency over the y-axis.

By more than method:

HeightNo. of treesHeight more thanC.F.
0 – 7260360
7 – 14275334
14 – 219210303
21 – 2813415268
28 – 3521620226
35 – 4228725144
42 – 493413073
49 – 563603519
Graph of Ogive

Question: 9

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

Profit (In lakhs In Rs)Number of shops (frequency)
More than or equal to 530
More than or equal to 1028
More than or equal to 1516
More than or equal to 2014
More than or equal to 2510
More than or equal to 307
More than or equal to 353

Draw both ogive for the above data and hence obtain the median.

Solution:

More than method:

Profit (In lakhs In Rs)Number of shops (frequency)
More than or equal to 530
More than or equal to 1028
More than or equal to 1516
More than or equal to 2014
More than or equal to 2510
More than or equal to 307
More than or equal to 353

Now, we mark on x-axis lower class limits, y-axis cumulative frequency. Thus, we plot the points (5, 30), (10, 28), (15, 16), (20, 14), (25,10), (30, 7) and (35, 3)

Less than method:

Profit in lakhsNo of shopsProfits less thanC.F
0 – 102102
10 – 15121514
15 – 2022016
20 – 2542520
25 – 3033023
30 – 3543527
35 – 4034030

Now we mark the upper class limits along x-axis and cumulative frequency along y-axis. Thus we plot the points (10, 2), (15,14), (20,16), (25, 20), (30, 23), (35, 27), (40, 30).

We find that the two types of curves intersect of P from point L it is drawn on x-axis The value of a profit corresponding to M is 17.5. Hence median is 17.5 lakh

Graph of Ogive

All Chapter RD Sharma Solutions For Class10 Maths

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