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#### Page No 623:

Statistics is the science which deals with the collection, presentation, analysis and interpretation of numerical data.

#### Page No 623:

The fundamental characteristics of data (statistics) are as follows:
(i) Numerical facts alone constitute data.
(ii) Qualitative characteristics like intelligence and poverty, which cannot be measured numerically, do not form data.
(iii) Data are aggregate of facts. A single observation does not form data.
(iv) Data collected for a definite purpose may not be suited for another purpose.
(v) Data in different experiments are comparable.

#### Page No 623:

Primary data: The data collected by the investigator himself with a definite plan in mind are known as primary data.
Secondary data: The data collected by someone other than the investigator are known as secondary data.

Primary data are highly reliable and relevant because they are collected by the investigator himself with a definite plan in mind,  whereas secondary data are collected with a purpose different from that of the investigator and may not be fully relevant to the investigation.

#### Page No 623:

(i) Variate : Any character which is capable of taking several different values is called a variant or a variable.
(ii) Class interval : Each group into which the raw data is condensed is called class interval .
(iii) Class size: The difference between the true upper limit and the true lower limit of a class is called its class size.
(iv) Class mark of a class: The class mark is given by .
(v) Class limit: Each class is bounded by two figures, which are called class limits.
(vi) True class limits: In the exclusive form, the upper and lower limits of a class are respectively known as true upper limit and true lower limit.
In the inclusive form of frequency distribution, the true lower limit of a class is obtained by subtracting 0.5 from the lower limit and the true upper limit of the class is obtained by adding 0.5 to the upper limit.
(vii) Frequency of a class: Frequency of a class is the number of times an observation occurs in that class.
(viii) Cumulative frequency of a class: Cummulative frequency of a class is the sum total of all the frequencies up to and including that class.

#### Page No 624:

(i)

 Blood group tally marks Number of students A 9 B 6 O 12 AB 3

(ii) AB is rarest and O is most common.

#### Page No 624:

 Number of heads tally marks Frequency 0 6 1 10 2 9 3 5

#### Page No 624:

The minimum observation is 0 and the maximum observation is 8.
Therefore, classes of  the same size covering the given data are 0-2, 2-4, 4-6 and 6-8.          .

Frequency distribution table:
 Class Tally mark Frequency 0-2 11 2-4 17 4-6 9 6-8 3

#### Page No 624:

(i)

 Class interval tally marks Frequency 0-5 10 5-10 13 10-15 5 15-20 2

(ii) As we can see from the table, there are 2 children who watched tv for 15 hours or more.

#### Page No 624:

The minimum observation is 0 and the maximum observation is 25.
Therefore, classes of the same size covering the given data are 0-5, 5-10, 10-15, 15-20 and 20-25.
Frequency distribution table:

 Class Tally mark Frequency 0-5 6 5-10 10 10-15 8 15-20 8 20-25 8

#### Page No 624:

The minimum observation is 6 and the maximum observation is 24.
Therefore, classes of the same size covering the given data are 6-9, 9-12, 12-15, 15-18, 18-21 and 21-24.
Frequency distribution table:
 Class Tally mark Frequency 6-9 5 9-12 4 12-15 4 15-18 7 18-21 3 21-24 7

#### Page No 624:

The minimum observation is 210 and the maximum observation is 330.
Therefore, classes of the same size covering the given data are 210-230, 230-250,250-270,270-290,290-310 and 310-330.
Frequency distribution table:

 Class Tally mark Frequency 210-230 4 230-250 4 250-270 5 270-290 3 290-310 7 310-330 5

#### Page No 625:

The minimum observation is 30 and the maximum observation is 120.

Frequency distribution table:

 Class Tally mark Frequency 30-40 4 40-50 6 50-60 3 60-70 5 70-80 9 80-90 6 90-100 2 100-110 3 110-120 2

Cumulative frequency table:

 Class Tally mark Frequency Cumulative frequency 30-40 4 4 40-50 6 10 50-60 3 13 60-70 5 18 70-80 9 27 80-90 6 33 90-100 2 35 100-110 3 38 110-120 2 40

#### Page No 625:

 Class tally marks Frequency Cumulative frequency 145-150 4 4 150-155 9 4 + 9 = 13 155-160 12 13 + 12 = 25 160-165 5 25 + 5 = 30

#### Page No 625:

The cumulative frequency table can be presented as given below:

 Age (in years ) No. of patients Cumulative frequency 10-20 90 90 20-30 50 140 30-40 60 200 40-50 80 280 50-60 50 330 60-70 30 360

#### Page No 625:

The grouped frequency table can be presented as given below:

 Marks No. of students 0-10 5 10-20 7 20-30 20 30-40 8 40-50 5 50-60 3

#### Page No 625:

The frequency table can be presented as given below:

 Marks Number of students 0-10 17 10-20 5 20-30 7 30-40 8 40-50 13 50-60 10

#### Page No 625:

The frequency table can be presented as below:

 Class Frequency 0-10 8 10-20 5 20-30 12 30-40 35 40-50 24 50-60 16

#### Page No 626:

Range = Maximum value $-$ minimu value
= 100 $-$ 46 = 54
Thus, the range is 54.

#### Page No 626:

(i)
(ii) mid-value = 10
width = 6
Let the lower limit of the class be x
upper limit = x + 6

$\frac{x+\left(x+6\right)}{2}=10\phantom{\rule{0ex}{0ex}}⇒x=7$
(iii) width = 5
lower class limit of lowest class = 10
The classes will be 10-15, 15-20, 20-25, 25-30, 30-35.
Upper class limit of the highest class = 35.
(iv) Class marks = 15, 20, 25, ...
class size = 20 $-$ 15 = 5
Let lower limit of class be x.
$\frac{x+\left(x+5\right)}{2}=20\phantom{\rule{0ex}{0ex}}⇒x=17.5$
Thus, the class is 17.5-22.5.
(v) 20 will be included in the class interval 20-30.

#### Page No 626:

The  complete table will be

Height (in cm) Frequency Cumulative frequency
160 – 165 15 a = 15
165 – 170 b = 35 – 15 = 20  35
170 – 175 12 = 35 + 12 = 47
175 – 180 d = 50 – 47 = 3 50
180 – 185 e = 55 – 50 = 5 55
185 –  190 5 f = 55 + 5 = 60
g = 15 + 20 + 12
+ 3 + 5 + 5 = 60

#### Page No 628:

(d) 26

We have:
Maximum value = 32
Minimum value = 6
We know:
Range = Maximum value $-$ Minimum value
=32 $-$ 6
=26

(b) 110

Class mark =

#### Page No 629:

(b) 2030
This is the continuous form of frequency distribution. Here, the upper limit of each class is excluded, while the lower limit is included. So, the number 20 is included in the class interval 2030.

#### Page No 629:

(b) 17.5$-$22.5

We are given frequency distribution 15, 20, 25, 30,...
Class size = 20 $-$ 15 = 5
Class marks = 20
Now,

Thus, the required class is 17.5$-$22.5.

#### Page No 629:

(b) 7

Given:
Mid value of the class = 10
Width of each class = 6
Now,
Let the lower limit be x.
We know:
Upper limit = Lower limit + Class size
= x + 6
Also,

Thus, the lower limit is 7.

#### Page No 629:

(a) 37–47

Let the lower limit be x.
Here,
Class size = 10
∴ Upper limit = Class size + Lower limit
Upper limit = (x + 10)
Mid value of the class interval = 42

#### Page No 629:

(a) 2m $-$ u

Given:
Mid value = m
Upper limit = u

We know:

#### Page No 629:

(c) 35

We have:
Class width = 5
Lower class limit of the lowest class = 10
Now,
Upper class limit of the highest class = 10 + 5 $×$ 5 = 35

#### Page No 629:

(c) 2m$-$L