Class 9 RD Sharma- Chapter 22 Tabular Representation of Statistical Data - Exercise 22.1 | Set 1

Question 1. What do you understand by the word “statistics” in:

(i) singular form (ii) plural form?

Solution:

The word statistics can be used in multiple ways, both singularly and plurally.

(i) In singular form, statistics can be used collectively as the science of collection, presentation, analysis, and interpretation of numerical data.

(ii) In plural form, statistics, however, implies numerical facts or observations that are collected together to serve a definite purpose.

Question 2. Describe some fundamental characteristics of statistics.

Solution:

Some fundamental characteristics of statistics are:

(1) Statistics are always collected with a definite purpose.

(2) Statistics are only expressed in quantitative and not qualitative terms.

(3) Statistics can be classified into various segments and often are comparable in an experiment.

Question 3. What are (i) primary data (ii) secondary data? Which of the two—the primary or the secondary data—is more reliable and why?

Solution:

(i) Primary data: The raw data collected without using any of the existing resources of the data by an investigator with a definite plan is called the primary data.

(ii)Secondary data: The data collected after using information from existing resources such as other published or unpublished sources is called secondary data.

Primary data is more reliable and relevant because it is raw in nature, collected without any prior information on the existing topic. It is original in nature, gathered by some individuals and/or the research bodies, whereas the secondary data are gathered by an individual or an institution for some purpose by taking help from existing resources and are used by someone else in another context.

Question 4. Why do we group data?

Solution: 

The data obtained in original form without any prior resources on the same, is called raw data. It is essentially difficult to capture information from the raw data, which is difficult to understand. Grouping of data increases the ease of understanding and interpretation. Also, it helps to simulate calculations on commodities which helps in describing and analyzing the data.

Question 5. Explain the meaning of the following terms:

(i) Variate

(ii) Class-interval

(iii) Class-size

(iv) Class-mark

(v) Frequency

(vi) Class limits

(vii)True class limits

Solution:

(i) Variate: Any character that can vary from one individual to another is called variate.

(ii) Class-interval: In the data of each group into which raw data is considered.

(iii) Class-size: The difference between the upper limit and lower limit of the specified class.

(iv) Class-mark: The middle value of the selected class is marked as the class-mark.

The following formula is used in its calculation :

Class-mark = (Upper limit + Lower limit) /2

(v) Frequency: The number of observations corresponding to a given class is known as frequency.

(vi) Class limits: Each class is bounded by two figures, called the class limits. The figure on the right side is called the upper limit while figure on the left side of the class is called the lower limit.

(vii)True class limits:

If classes are inclusive. For example 5-9, 10-14, 15-19, and so on

Then, the true lower limit of class = Lower limit of class – 0.5

Also, the true upper limit of class = Upper limit of class + 0.5

In this case, the True limits of the class are 5-9 are 4.5 and 9.5

But, if classes are exclusive like 20-30, 30-40, 40-50, etc., then class limits and true class limits are equivalent.

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?

Solution:

The given ages of ten students of a group are as follows:

8 – 6, 9 – 0, 8 – 4, 9 – 3, 7 – 8, 8 – 11, 8 – 7, 9 – 2, 7 – 10, 8 – 8.

(i) The Lowest age in the given group = 7 years 8 months

(ii) The Highest age in the given group = 9 years 3 months

(iii) Range = The Highest age – The Lowest age

Substituting the values,

 Range = (9 years 3 months) – (7 years 8 months)

           = 1 year 7 months

Question 7. The monthly pocket money of six friends is given below:

Rs 45, Rs 30, Rs 40, Rs 50, Rs 25, Rs 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.

Solution:

The monthly pocket money of six friends are given below in the form of a sequence:

Rs 45, Rs 30, Rs 40, Rs 50, Rs 25, Rs 45

(i) The Highest pocket money given = Rs 50

(ii) The Lowest pocket money given = Rs 25

(iii) Range = The Highest pocket money – The Lowest pocket money

Substituting the values, we get,

= Rs 50 – Rs 25

= Rs 25

(iv) Arranging the amounts of pocket money in ascending order is: Rs 25, Rs 30, Rs 40, Rs 45, Rs 45,Rs 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, 0.25-00.50, 0.50-0.75

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

Solution:

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

Since, the given classes are inclusive, so

True lower limit of class = Lower limit of class – 0.5

And, True upper limit of class = Upper limit of class + 0.5

True class limits are 0.5-4.5, 4.5-9.5, 9.5-14.5

Therefore, class size = 14.5 – 9.5 = 5

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

Since, classes are inclusive, so

True lower limit of class = Lower limit of class – 0.5

And, True upper limit of class = Upper limit of class + 0.5

True class limits 19.5-19.5, 19.5-29.5, 29.5-29.5

The required class size = 39.5-29.5 = 10

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

Here the class limits and true class limits are the same

So, the required class size = 120 – 100 = 20

(iv) 0-0.25, 0.25-00.50, 0.50-0.75

Here the class limits and true class limits are the same

So, the required class size = 0.25 – 0 = 0.25

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

Therefore, class limits and true class limits are the same

So, class size = 5.01 – 5.0 = 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 ascending order, 30 to 39 one group,40 to 49-second groups, 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?

Solution:

(i) Arrange marks in ascending order:

Class Marks	Observations	Frequency
30-39	37, 39	2
40-49	44,48,48	3
50-59	50, 52, 53, 55, 56, 58, 58, 59	8
60-69	60, 60, 60, 61, 62, 64, 67, 68	8
70-79	70, 75, 77, 78	4
80-89	84,88	2
90-99	90, 98	2
100-109	100	1

(ii) Therefore, from the table above, it is observed that, the Highest score is equal to 100,

(iii) The Lowest score Is equal to 37.

(iv) Since, the range is defined as:

Range = The Highest score – The Lowest score 

           = 100 – 37 

           = 63

(v) 2

(vi) 8

(vii) 51, 54, 57

(viii) 5

Question 10. The weights of newborn 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 highest weight.

(ii) Determine the highest weight.

(iii) Determine the lowest weight.

(iv) Determine the range.

(v) How many babies were born 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?

Solution:

(i) Arrange weights in descending order:

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) The Highest weight in the given sequence= 3.1 Kg

(iii) The Lowest weight in the given sequence= 2.1 Kg

(iv) Range in the given sequence = 3.1 kg – 2.1 kg = 1.0 Kg

(v) 15 babies were born on that particular day.

(vi) 4 babies out of all weigh below 2.5 Kg.

(vii) Babies with more than 2.8 Kg weight are 4 in number.