The NCERT Solution for Class 11 maths includes answers to every question from the NCERT text book’s exercise. Top students love SWC NCERT Solutions because they are very effective. In general, Class 11 is regarded as the most significant year in a student’s professional development. The NCERT answers for class 11 maths were created with the goal of providing students with the most help possible.

Answers to the class 11 maths questions provided in the exercise might be challenging for students for a number of reasons. One should not omit any NCERT textbook content in order to get the highest possible grade. Use the Swastik Classes’ NCERT answers for   maths class 11 as a resource. Important exam-based questions are covered in depth in each chapter.

NCERT Solutions for Class-11 Maths Exercise 15.1

Question1. Find the mean deviation about the mean for the data

4, 7, 8, 9, 10, 12, 13, 17

Solution :
The given data is

4, 7, 8, 9, 10, 12, 13, 17

chapter 15-Statistics Exercise 15.1
/chapter%2015_html_mdbbe6c6.gif

Question2. Find the mean deviation about the mean for the data

38, 70, 48, 40, 42, 55, 63, 46, 54, 44

Solution :
The given data is

38, 70, 48, 40, 42, 55, 63, 46, 54, 44

Mean of the given data,

chapter 15-Statistics Exercise 15.1

The deviations of the respective observations from the mean chapter 15-Statistics Exercise 15.1are

–12, 20, –2, –10, –8, 5, 13, –4, 4, –6

The absolute values of the deviations, i.e. chapter 15-Statistics Exercise 15.1, are

12, 20, 2, 10, 8, 5, 13, 4, 4, 6

The required mean deviation about the mean is

chapter 15-Statistics Exercise 15.1

Question3. Find the mean deviation about the median for the data.

13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

Solution :
The given data is

13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

Here, the numbers of observations are 12, which is even.

Arranging the data in ascending order, we obtain

10, 11, 11, 12, 13, 13, 14, 16, 16, 17, 17, 18

The number of observations is 12

Then,

Median = ((12/2)th observation + ((12/2)+ 1)th observation)/2

(12/2)th observation = 6th = 13

(12/2)+ 1)th observation = 6 + 1

= 7th = 14

Median = (13 + 14)/2

= 27/2

= 13.5

So, the absolute values of the respective deviations from the median, i.e., |xi – M| are

3.5, 2.5, 2.5, 1.5, 0.5, 0.5, 0.5, 2.5, 2.5, 3.5, 3.5, 4.5

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 5

Mean Deviation,

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 6

= (1/12) × 28

= 2.33

Question4. Find the mean deviation about the median for the data

36, 72, 46, 42, 60, 45, 53, 46, 51, 49

Solution :

First we have to arrange the given observations into ascending order,

36, 42, 45, 46, 46, 49, 51, 53, 60, 72.

The number of observations is 10

Then,

Median = ((10/2)th observation + ((10/2)+ 1)th observation)/2

(10/2)th observation = 5th = 46

(10/2)+ 1)th observation = 5 + 1

= 6th = 49

Median = (46 + 49)/2

= 95

= 47.5

So, the absolute values of the respective deviations from the median, i.e., |xi – M| are

11.5, 5.5, 2.5, 1.5, 1.5, 1.5, 3.5, 5.5, 12.5, 24.5

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 7

Mean Deviation,

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 8

= (1/10) × 70

= 7

So, the mean deviation about the median for the given data is 7.

Question5. Find the mean deviation about the mean for the data.

xi510152025
fi74635

Solution :

xififi xiNCERT Solutions for Class 11 Maths Chapter 15 StatisticsNCERT Solutions for Class 11 Maths Chapter 15 Statistics
5735963
10440416
1569016
20360618
2551251155
 25350 158
NCERT Solutions for Class 11 Maths Chapter 15 Statistics

Question6. Find the mean deviation about the mean for the data

xi1030507090
fi42428168

Solution :

xififxiNCERT Solutions for Class 11 Maths Chapter 15 StatisticsNCERT Solutions for Class 11 Maths Chapter 15 Statistics
1044040160
302472020480
5028140000
7016112020320
90872040320
 804000 1280
NCERT Solutions for Class 11 Maths Chapter 15 Statistics

Question7. Find the mean deviation about the median for the data.

xi579101215
fi862226

Solution :
The given observations are already in ascending order.

Adding a column corresponding to cumulative frequencies of the given data, we obtain the following table.

xific.f.
588
7614
9216
10218
12220
15626
|x– M|202358
fi862226
 fi |xi – M|160461048

Now, N = 26, which is even.

Median is the mean of the 13th and 14th observations. Both of these observations lie in the cumulative frequency 14, for which the corresponding observation is 7.

Then,

Median = (13th observation + 14th observation)/2

= (7 + 7)/2

= 14/2

= 7

So, the absolute values of the respective deviations from the median, i.e., |xi – M| are shown in the table.

.NCERT Solutions for Class 11 Maths Chapter 15 Statistics
 

Question8. Find the mean deviation about the median for the data

xi 1521273035
fi 35678

Solution :
The given observations are already in ascending order.

Adding a column corresponding to cumulative frequencies of the given data, we obtain the following table.

xi fc.f.
1533
2158
27614
30721
35829

Here, N = 29, which is odd.

  |xi – M|159305
 fi35678
 fi |xi – M|454518040

Now, N = 29, which is odd.

So 29/2 = 14.5

The cumulative frequency greater than 14.5 is 21, for which the corresponding observation is 30.

Then,

Median = (15th observation + 16th observation)/2

= (30 + 30)/2

= 60/2

= 30

So, the absolute values of the respective deviations from the median, i.e., |xi – M| are shown in the table.

NCERT Solutions for Class 11 Maths Chapter 15 Statistics

Question9. Find the mean deviation about the mean for the data.

Income per dayNumber of persons
0-1004
100-2008
200-3009
300-40010
400-5007
500-6005
600-7004
700-8003

Solution :
The following table is formed.

Income per dayNumber of persons fiMid-point xifi xiNCERT Solutions for Class 11 Maths Chapter 15 StatisticsNCERT Solutions for Class 11 Maths Chapter 15 Statistics
0 – 1004502003081232
100 – 200815012002081664
200 – 30092502250108972
300 – 400103503500880
400 – 5007450315092644
500 – 60055502750192960
600 – 700465026002921168
700 – 800375022503921176
 50 17900 7896

Here,

NCERT Solutions for Class 11 Maths Chapter 15 Statistics

Question10. Find the mean deviation about the mean for the data

Height in cmsNumber of boys
95-1059
105-11513
115-12526
125-13530
135-14512
145-15510

Solution :
The following table is formed.

Height in cmsNumber of boys fiMid-point xifxiNCERT Solutions for Class 11 Maths Chapter 15 StatisticsNCERT Solutions for Class 11 Maths Chapter 15 Statistics
95-105910090025.3227.7
105-11513110143015.3198.9
115-1252612031205.3137.8
125-1353013039004.7141
135-14512140168014.7176.4
145-15510150150024.7247
NCERT Solutions for Class 11 Maths Chapter 15 Statistics

Question11. Find the mean deviation about median for the following data:

MarksNumber of girls
0-106
10-208
20-3014
30-4016
40-504
50-602

Solution :
The following table is formed.

MarksNumber of girls fiCumulative frequency (c.f.)Mid-point xi|xi – Med.|
 
f|xi – Med.|
0-1066522.85137.1
10-208141512.85102.8
20-301428252.8539.9
30-401644357.15114.4
40-504484517.1568.6
50-602505527.1554.3
 50   517.1

The class interval containing Nth/2 or 25th item is 20-30

So, 20-30 is the median class.

Then,

Median = l + (((N/2) – c)/f) × h

Where, l = 20, c = 14, f = 14, h = 10 and n = 50

Median = 20 + (((25 – 14))/14) × 10

= 20 + 7.85

= 27.85

NCERT Solutions for Class 11 Maths Chapter 15 Statistics

Question12. Calculate the mean deviation about median age for the age distribution of 100 persons given below:

AgeNumber
16-205
21-256
26-3012
31-3514
36-4026
41-4512
46-5016
51-559

Solution :
The given data is not continuous. Therefore, it has to be converted into continuous frequency distribution by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of each class interval.

The table is formed as follows.

AgeNumber fiCumulative frequency (c.f.)Mid-point xi|xi – Med.|fi |x– Med.|
15.5-20.5551820100
20.5-25.5611231590
25.5-30.512232810120
30.5-35.5143733570
35.5-40.526633800
40.5-45.5127543560
45.5-50.516914810160
50.5-55.591005315135
 100   735

The class interval containing Nth/2 or 50th item is 35.5 – 40.5

So, 35.5 – 40.5 is the median class.

Then,

Median = l + (((N/2) – c)/f) × h

Where, l = 35.5, c = 37, f = 26, h = 5 and N = 100

Median = 35.5 + (((50 – 37))/26) × 5

= 35.5 + 2.5

= 38

NCERT Solutions for Class 11 Maths Chapter 15 Statistics

Conclusiosn for NCERT SOLUTIONS FOR CLASS 11 MATHS CHAPTER 15-STATISTICS EXERCISE 15.1

An academic team of knowledgeable members of SWC has produced and published the NCERT Solutions for class 11’s  maths chapter for your use as a reference. You can get answers to all of the chapters of the NCERT maths class 11 here at SWC. Please make use of the following NCERT answers that were created by SWC as a reference for this chapter. In addition to that, study the chapter’s theory before attempting to solve the NCERT problems.

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