Class 11 Statistics NCERT Solutions for Chapter 5 2023: Download Free PDF

NCERT Solutions for Class 11 Statistics Chapter 5: We offer students with an excellent understanding of statistics. They offer up-to-date and improved solutions, with content prepared by subject matter specialists with years of experience. With the help of NCERT Solutions For Class 11 Statistics Chapter 5, students can obtain information as well as good grades.

NCERT Solutions for Class 11 Statistics Chapter 5 PDF

NCERT Solutions For Statistics Class 11 Ch 5

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NCERT Solutions for Class 11 Statistics Chapter 5: Overview

Class 11 Statistics NCERT Solutions Chapter 5 is free to download in PDF format from our official website. Students should take advantage of this opportunity to learn more. It is up to the student whether to use a soft copy or a hard copy. If they are willing to study from a physical copy, they will be able to learn without having to worry about their internet connection. It also helps to prepare for competitive exams and other board exams.

Measures of Central Tendency

1. Introduction 

Class 11 Statistics NCERT Solutions As the students have learned how to gather data and portray data, Chapter 5 aims to introduce the measures available for the central tendency in Statistics. The following step is to analyze and interpret the data. We can use three different measures of central trends to assess the data: arithmetic means, median, and mode.

2. Arithmetic Mean

The arithmetic mean is a widely used metric for determining the average of a set of data. The mean for grouped data and the mean for ungrouped data are two different versions explained in NCERT Solutions for Class 11 Statistics Chapter.

5. The arithmetic mean is the sum The NCERT Solutions Class 11 Statistics Chapter 5 clearly explains available on our official website with an illustration. Again the grouped data has two kinds of series namely-discrete series and continuous series.

There are three methods for computing the mean for ungrouped and grouped data, according to the Measures of Central Tendency in Statistics Class 11 NCERT Solutions. The three possibilities are a direct methodology, an assumed method, and a step division method. Each strategy may alter depending on whether the data is grouped or ungrouped.

3. Median

The students are urged to master another measure of central tendency, the median, in this section. The median is a straightforward concept, according to the NCERT Class 11 Statistics Chapter 5 Measures of Central Tendency. It can be computed by taking the middle value, which is the value that divides both sides of the values. However, this is only conceivable if the series’ length is odd. If students are asked to find the median for a set of even number values, we must first find the average of the two middle words. 

Another topic covered with the students is quartiles. The term quartile refers to the division of a full size into four equal pieces. It can be calculated separately for both series by themselves. Percentiles are a topic for which the whole size is divided into 99 Parts which reaches the cent. 

4. Mode 

Our NCERT solutions for Statistics Chapter 5 in Class 11 specify that students comprehend each measure of central tendency. Because it is impossible for kids to forget the meaning and formula if they grasp them. Despite the fact that the mode is the last measure of central tendency, it is quite important.

The mode is a French word that refers to the most popular or common value in the set. In simple terms, the mean is the value with the greatest number of occurrences. We can calculate directly using the direct technique by looking at itself. There is a specific formula for determining the value of mode in the continuous approach.

5. The relative position of arithmetic mean, median, and mode

The placements of three measures of central tendency are also mentioned in the NCERT Solutions For Class 11 Statistics Chapter 5. The median should be in the middle of the magnitude of three measures can be stirred in any direction. The arithmetic means and mode will be at one of the two extremes.

6. Conclusion

Thus Chapter 5 of measures of central tendency has been explained very well by professional teachers to the students. The material is provided with different examples of all six concepts.

Access NCERT Solutions For Class 11 Statistics Chapter 5

Question 2(ii):

Which average is affected most by the presence of extreme items?

(a) median

(b) mode

(c) arithmetic mean

(d) geometric mean

(e) harmonic mean

ANSWER:

Arithmetic mean is the most affected by the presence of extreme items. It is one of the prime demerits of the arithmetic mean. It is easily distorted by the extreme values, and also the value of arithmetic mean may not figure out at all in the series.

Page No 72:

Question 2(iii):

The algebraic sum of deviation of a set of n values from A.M. is

(a) n

(b) 0

(c) 1

(d) none of the above

ANSWER:

The algebraic sum of deviation of a set of n values from A.M. is zero. This is one of the mathematical properties of arithmetic mean.

Page No 72:

Question 3:

Comment whether the following statements are true or false.

(i) The sum of deviation of items from median is zero.

(ii) An average alone is not enough to compare series.

(iii) Arithmetic mean is a positional value.

(iv) Upper quartile is the lowest value of top 25% of items.

(v) Median is unduly affected by extreme observations.

ANSWER:

(i) The sum of deviation of items from median is zero. False

The statement is false. This mathematical property applies to the arithmetic mean that states that the sum of the deviation of all items from the mean is zero.

(ii) An average alone is not enough to compare series. True

An average indicates only the behaviour of a particular series. Therefore, in order to measure the extent of divergence of different items from the central tendency is measured by dispersion. So, average is not enough to compare the series.

(iii) Arithmetic mean is a positional value. False

This statement is false as mean is not a positional average, rather the statement holds true for median and mode. The calculation of median and modal values is based on the position of the items in the series, i.e. why these are also termed as positional averages.

(iv) Upper quartile is the lowest value of top 25% of items. True

The value that divides a statistical series into four equal parts, the end value of each part is called quartile. The third quartile or the upper quartile has 75 % of the items below it and 25 % of items above it,

(v) Median is unduly affected by extreme observations. False

This statement is true for Arithmetic mean. Arithmetic mean is most affected by the presence of extreme items. It is one of the prime demerits of the arithmetic mean. It is easily distorted by the extreme values, and also the value of arithmetic mean may not figure out at all in the series.

Page No 72:

Question 4:

If the arithmetic mean of the data given below is 28, find (a) the missing frequency, and (b) the median of the series:

Profit per retail shop (in Rs)	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60
Number of retail shops	12	18	27	–	17	6

 

ANSWER:

(i) Let the missing frequency be f₁ 

Arithmetic Mean = 28

 

 

Profit per Retail Shop (in Rs)	No of Retail Shops	Mid Value
Class Interval	(f)	(m)	fm
0 – 10	12	5	60
10 – 20	18	15	270
20 – 30	27	25	675
30 – 40	f1	35	35f1
40 – 50	17	45	765
50 – 60	6	55	330

 

or, 2240 + 28f₁ = 2100 + 35f₁

or, 2240 – 2100 = 35f₁ – 28f₁

or, 140 = 7f₁

f₁ = 20

 

(ii)

	Class Interval	Frequency   (f)	Cumulative Frequency (CF)
	0 – 10	12	12
	10 – 20	18	30
	20 – 30	27	57
	30 – 40	20	77
	40 – 50	17	94
	50 – 60	6	100
	Total

 

So, the Median class = Size of  item

                                         = 50^th item

50^th item lies in the 57^th cumulative frequency and the corresponding class interval is 20 – 30.

 

Page No 72:

Question 5:

The following table gives the daily income of ten workers in a factory. Find the arithmetic mean.

Workers	A	B	C	D	E	F	G	H	I	J
Daily Income (in Rs)	120	150	180	200	250	300	220	350	370	260

 

ANSWER:

Workers	Daily Income (in Rs) (X)
A	120
B	150
C	180
D	200
E	250
F	300
G	220
H	350
I	370
J	260
Total

 

N = 10

Arithmetic mean = Rs 240

Page No 72:

Question 6:

Following information pertains to the daily income of 150 families. Calculate the arithmetic mean.

Income (in Rs)	Number of families
More than 75	150
More than 85	140
More than 95	115
More than 105	95
More than 115	70
More than 125	60
More than 135	40
More than 145	25

 

ANSWER:

Income	No. of families	Frequency	Mid Value	fm
Class Interval	(CF)	(f)	(m)
75 – 85	150	150 – 140 = 10	80	800
85 – 95	140	140 – 115 = 25	90	2250
95 – 105	115	115 – 95 = 20	100	2000
105 – 115	95	95 – 70 = 25	110	2750
115 – 125	70	70 – 60 = 10	120	1200
125 – 135	60	60 – 40 = 20	130	2600
135 – 145	40	40 – 25 = 15	140	2100
145 – 155	25	25	150	3750
Total

 

= Rs 116.33

Page No 73:

Question 7:

The size of land holdings of 380 families in a village is given below. Find the median size of land holdings.

Size of Land Holdings (in acres)	Less than 100	100 – 200	200 – 300	300 – 400	400 and above
Number of families	40	89	148	64	39

 

ANSWER:

Size of Land Holdings Class Interval	No. of Families   (f)	Cumulative Frequency (CF)
0 – 100	40	40
100 – 200	89	129
200 – 300	148	277
300 – 400	64	341
400 – 500	39	380
Total

 

So, the Median class = Size of  item = 190^th item

 

190^th item lies in the 129^th cumulative frequency and the corresponding class interval is 200 – 300.

The median size of land holdings = 241.22 acres

Page No 73:

Question 8:

The following series relates to the daily income of workers employed in a firm. Compute (a) highest income of lowest 50% workers (b) minimum income earned by the top 25% workers and (c) maximum income earned by lowest 25% workers.

Daily Income (in Rs)	10 – 14	15 – 19	20 – 24	25 – 29	30 – 34	35 – 39
Number of workers	5	10	15	20	10	5

(Hint: Compute median, lower quartile and upper quartile)

ANSWER:

Daily Income (in Rs) Class Interval	No. of Workers (f)	Cumulative frequency (CF)
9.5 – 14.5	5	5
14.5 – 19.5	10	15
19.5 – 24.5	15	30
24.5 – 29.5	20	50
29.5 – 34.5	10	60
34.5 – 39.5	5	65

 

(a) Highest income of lowest 50% workers

 

 

32.5^th item lies in the 50^th cumulative frequency and the corresponding class interval is 24.5 – 29.5.

 

 

(b) Minimum income earned by top 25% workers
In order to calculate the minimum income earned by top 25% workers, we need to ascertain Q₃.

48.75^th item lies in 50^th item and the corresponding class interval is 24.5 – 29.5.

 

 

(c) Maximum  income earned by lowest 25% workers
In order to calculate the maximum income earned by lowest 25% workers, we need to ascertain Q₁.

  

16.25^th item lies in the 30^th cumulative frequency and the corresponding class interval is 19.5 – 24.5

Page No 73:

Question 9:

The following table gives production yield in kg. per hectare of wheat of 150 farms in a village. Calculate the mean, median and mode values.

Production yield (kg. per hectare)	50 – 53	53 – 56	56 – 59	59 – 62	62 – 65	65 – 68	68 – 71	71 – 74	74 – 77
Number of farms	3	8	14	30	36	28	16	10	5

 

ANSWER:

(i) Mean

Production Yield	No. of farms	Mid value	A = 63.5
50 – 53	3	51.5	–12	–4	–12
53 – 56	8	54.5	–9	–3	–24
56 – 59	14	57.5	–6	–2	–28
59 – 62	30	60.5	–3	–1	–30
62 – 65	36	63.5	0	0	0
65 – 68	28	66.5	+3	+1	28
68 – 71	16	69.5	+6	+2	32
71 – 74	10	72.5	+9	+3	30
74 – 77	5	75.5	+12	+4	20
Total

 

= 63.5 + 0.32

= 63.82 kg per hectare

 

(ii) Median

 

Class Interval	Frequency (f)	CF
50 – 53	3	3
53 – 56	8	11
56 – 59	14	25
59 – 62	30	55
62 – 65	36	91
65 – 68	28	119
68 – 71	16	135
71 – 74	10	145
74 – 77	5	150
Total

 

75^th item lies in the 91^st cumulative frequency and the corresponding class interval is 62 – 65.

 

 (iii) Mode

 

Grouping Table
Class Interval	I	II	III	IV	V	VI
50 – 53	3
		11	22	25	52
53 – 56	8
56 – 59	14
		44
59 – 62	30
62 – 65
			44			54
65 – 68	28
68 – 71	16
		26	15	31
71 – 74	10
74 – 77	5

  

                                                                                              Analysis Table

 

Column	50 – 53	53 – 56	56 – 59	59 – 62	62 – 65	65 – 68	68 – 71	71 – 74	74 – 77
I					√
II					√	√
III				√	√
IV				√	√	√
V					√	√	√
VI			√	√	√
Total	–	–	1	3	6	3	1	–	–

 

Modal class = 62 – 65

 

Access Other Chapters of NCERT Solutions For Class 11 Statistics

You can download the PDF of NCERT Solutions For Class 11 Statistics Other Chapters:

• Chapter-1 Introduction
• Chapter-2 Collection Of Data
• Chapter-3 organization Of Data
• Chapter-4 Presentation of Data
• Chapter-6 Measures of Dispersion
• Chapter-7 Correlation
• Chapter-8 Index Numbers
• Chapter-9 Use of Statistical Tool

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