Primary data are reliable and relevent because they are original in character and are collected by some individuals or by some institutions or by research bodies.

Question - 4 : - Why do we group data?

Answer - 4 : - When the number of observations is large, then arranging data in ascending or descending order is tedius job and it does not tell us much except minimum or maximum(s) of data. So, to make it easily understandable and clear, we tabulate data in the form of a table.

Question - 5 : -
Explain the meaning of the following terms:
(i) variate
(ii) class intervals
(iii) class size
(iv) class mark
(v) frequency
(vi) class limits
(vii) true class limits.

Answer - 5 : -

(i) Variate : The observations of a data are called variate.

(ii) Class intervals : When the presentations of data in classes, or groups, then groups are called classes or class intervals.

(iii) Class size : The difference between upper limit and lower limit is called class size.

(iv) Class mark : The mean of lower limit and upper limit is called class mark or mid value. Therefore class mark

(v) Frequency : The number of times an observation occurs in the given data, is called frequency of that observation.

(vi) Class limits : Every class has two limits : lower limit and upper limit.

(vii) True class limits : Whenever inclusive method is used, it is necessary tp make an adjustment to determine the correct class intervals, and to have continuity. If a-b is a class in inclusive method, then in order to change it into exclusive method, it becomes

[lower limit of a class – upper limit of previous class]

Question - 6 : -
The ages of ten students of a group are given below. The ages have been recorded in years and months.
8-6, 9-0, 8-4, 9-3, 7-8, 8-11, 8-7, 9-2, 7¬10, 8-8
(i) What is the lowest age?
(ii) What is the highest age?
(iii) Determine the range?

Answer - 6 : -

From the given data

(i) Lowest age is 7 years 8 months

(ii) The highest age is 9 years, 3 months

(iii) Range = Highest term – Lowest term

= 9 years 3 months – 7 years 8 months

= 1 years 7 months

Question - 7 : -
The monthly pocket money of six friends is given below:
₹45, ₹30, ₹40, ₹50, ₹25, ₹45
(i) What is the highest pocket money?
(ii) What is the lowest pocket money?
(iii) What is the range?
(iv) Arrange the amounts of pocket money in ascending order.

Answer - 7 : -

From the given data

(i) Highest pocket money = ₹50

(ii) Lowest pocket money = ₹25

(iii) Range = Highest term – Lowest term = ₹50-₹25 = ₹25

(iv) In ascending order : ₹25, ₹30, ₹40, ₹45, ₹45, ₹50

Question - 8 : -
Write the class-size in each of the following:
(i) 0-4,5-9,10-14
(ii) 10-19, 20-29, 30-39
(iii) 100-120, 120-140, 160-180
(iv) 0-0.25, 0.25-0.50, 0.50-0.75
(v) 5-5,01, 5.01-5.02, 5.02-5.03

Answer - 8 : -

(i) In 0-4, 5-9, 10-14

0-4 means from 0 to 4, similarly 5-9 means 5 to 9 and 10-14 means 10 to 14

class-size is 5

(ii) In 10-19, 20-29, 30-39

Here 10-19, means 10 to 19, 20-29 means 20 to 29 and 30-39 means 30 to 39

Class-size = 10

(iii) 100-120, 120-140, 160-180

Here 100-120, 120-140, 160-180

Then 120 – 100 = 20, 140 – 120 = 20, 180 – 160 = 20 is class-size = 20

(iv) 0-0.25, 0.25-0.50, 0.50-0.75

Here 0.25 – 0 = 0.25, 0.50 – 0.25 = 0.25 and 0.75 – 0.50 = 0.25

∴ Class-size = 0.25

(v) 5-5.01, 5.01-5.02, 5.02-5.03

Here 5.01 – 5 = 0.01, 5.02 – 5.01 = 0.01 and 5.03 – 5.02 = 0.01

∴ Class-size = 0.01

Question - 9 : -
The final marks in mathematics of 30 students are as follows:
53, 61, 48, 60, 78, 68, 55, 100, 67, 90
75, 88, 77, 37, 84, 58, 60, 48, 62, 56
44, 58, 52, 64, 98, 59, 70, 39, 50, 60
(i) Arrange these marks in the ascending order,30 to 39 one group, 40 to 49 second group, etc.
Now answer the following:
(ii) What is the highest score?
(iii) What is the lowest score?
(iv) What is the range?
(v) If 40 is the pass mark how many have failed?
(vi) How many have scored 75 or more?
(vii) Which observations between 50 and 60 have not actually appeared?
(viii)How many have scored less than 50?

Answer - 9 : -

(i) Arranging in ascending order:

37, 39, 44, 48, 48, 50, 52, 53, 55, 56, 58, 58, 59, 60, 60, 60, 61, 62, 64, 67, 68, 70, 75, 77, 78, 84, 88, 90, 98, 100

(ii) Highest score =100

(iii) Lowest score = 37

(iv) Range = Highest score – Lowest score = 100 – 37 = 63

(v) If 40 is marks, then the number of students who failed = 2

(vi) No. of students who scored 75 or more = 8

(vii) Between 50 and 60, the scores which are missing 51, 54, 57

(viii) Number of students who scored less then 50 = 2 + 3 = 5

Question - 10 : -
The weights of new born babies (in kg) in a hospital on a particular day are as follows:
2.3, 2.2, 2.1, 2.7, 2.6, 3.0, 2.5, 2.9, 2.8, 3.1, 2.5, 2.8, 2.7, 2.9, 2.4
(i) Rearrange the weights in descending order.
(ii) Determine the highest weight.
(iii) Determine the lowest weight.
(iv) Determine the range.
(v) How many babies were bom on that day?
(vi) How many babies weigh below 2.5 kg?
(vii) How many babies weigh more than 2.8 kg?
(viii)How many babies weigh 2.8 kg?

Answer - 10 : -

(i) Weights in descending order are

3.1, 3.0, 2.9, 2.9, 2.8, 2.8, 2.7, 2.7, 2.6, 2.5, 2.5, 2.4, 2.3, 2.2, 2.1

(ii) Highest weight = 3.1

(iii) Lowest weight = 2.1

(iv) Range = Highest weight – Lowest wight = 3.1 – 2.1 = 1.0

(v) No. of babies who bom = 15

(vi) No. of babies whose weights are below 2.5 kg = 4

(vii) No. of babies whose weight are more than 2.8 kg = 4.

(viii) No. of babies whose weight is 2.8 kg = 2

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RD Chapter 22 Tabular Representation of Statistical Data Ex 22.1 Solutions

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