RD Sharma 2020 solution class 9 chapter 22 Tabular Representation of Statistical Data Exercise 22.1

Exercise 22.1

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Question 1:

What do you understand by the word ''statistics'' in

(i) singular form       (ii) plural form?

Answer 1:

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

(ii) In plural form statistics means numerical facts or observations collected with definite purpose.

For examples, the income and expenditure of persons in a particular locality, number of males and females in a particular town are statistics.

Question 2:

Describe some fundamental characteristic of statistics.

Answer 2:

The plural form statistics has the simplest structure and the singular form statistics has many components. There is only structural difference between singular and plural form statistics. Some of the characteristics of a statistics are

1. Statistics is a collection of observations. So, clearly a single observation cannot form a statistics.

2. Statistics are collected with definite purpose.

3. Statistics are comparable and classified into various types depending on their properties.

4. Statistics are expressed quantitatively and not qualitatively. 

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?

Answer 3:

(i) When an investigator collects data himself with a definite plan or designs in his (her) mind, it is called primary data.

(ii) Data which are not originally collected rather obtained from published or unpublished sources are known as secondary data.

 

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Question 4:

Why do we group data?

Answer 4:

To study the features of a collected data, the data must be arranged in a condensed form. There are a number of ways to arrange the data in condensed form, namely,

1. Serial order or alphabetical order

2. Ascending order

3. Descending order

But, if the number of observations is large, then arranging data in ascending or descending or serial order is a tedious job and it does not tell us much except perhaps the minimum(s) and maximum(s) of data. So to make it easily understandable and clear we condense the data into groups or table form.

Question 5:

Explain the meaning of the following terms:

(i) variate

(ii) class-integral

(iii) class-size

(iv) class-mark

(v) frequency

(vi) class limits

(vii) true class limits.

Answer 5:

(i) A name which takes different values is called variates. For example, the mark obtained by students of class IX in mathematics is variates.

(ii) In a grouped data, the groups are called class-intervals. For example, 0-5, 5-10, 10-15… are class intervals.

(iii) The difference between the true upper limit and the true lower limit of a class is called its class size. For example, the class size of the class-interval 10-15 is

(iv) The mid value of a class is called the class mark. For example, the mid value of the class 10-15 is

(v) The number of observation falling in a particular class is called the frequency of that class or class frequency. For example, if the number of students obtaining marks 60-70 in a particular subject is 60, then the frequency of the class 60-70 is 60.

(vi) Class limits are the boundaries of a class. The left boundary of a class is called the lower limit and the right boundary of a class is called the upper limit. For example, for the class interval 60-70 the lower limit is 60 and the upper limit is 70.

(vii) The class limits of a continuous grouped frequency distribution are called true class limits. For example, 5-10, 10-15, 15-20, 20-25, 25-30 are continuous class intervals, then the true lower and upper limits (class limits) of the class 15-20 are 15 and 20 respectively. If the classes are not continuous, then adjust the class intervals to form continuous grouped class intervals.

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 - 0,4, 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:

After arranging in ascending order, the ages of the students are 7 years 8 months, 7 years 10 months, 8 years 4 months, 8 years 6 months, 8 years 7 months, 8 years 8 months, 8 years 11 months, 9 years, 9 years 2 months, and 9 years 3 months.

(i) The lowest age is 7 years 8 months.

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

(iii) The range of the ages is

Question 7:

The monthly pocket money of six friends is given below:
Rs 45, Rs 30, Rs 50, Rs 25, Rs 45

(a) What is the highest pocket money?

(b) What is the lowest pocket money?

(c) What is the range?

(d) Arrange the amounts of pocket money in ascending order.

Answer 7:

(i) After arranging in ascending order, the pocket money’s in Rs. are 25, 30, 40, 45, 45 and 50. The highest pocket money is Rs 50.

(ii) The lowest pocket money is Rs 25.

(iii) The range of the pocket money’s is

(iv) The given data (pocket money in Rs.) in ascending order is 25, 30, 40, 45, 45 and 50.

Question 8:

Write the class-size in each of the following:

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

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

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

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

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

Answer 8:

(i) The given classes are 0-4, 5-9 and 10-14. The classes can be written in continuous form as (-0.5)-4.5, 4.5-9.5, and 9.5-14.5. The upper and lower limits of the first class are 4.5 and (-0.5) respectively. Hence, the class size is

(ii) The given classes are 10-19, 20-29, and 30-39. The classes can be written in continuous form as 9.5-19.5, 19.5-29.5, 29.5-39.5. The upper and lower limits of the first class are 19.5 and 9.5 respectively. Hence, the class size is

(iii) The given classes are 100-120, 120-140, 160-180, are in continuous form. The upper and lower limits of the first class are 120 and 100 respectively. Hence, the class size is

(iv) The given classes are 0-0.25, 0.25-0.50, 0.50-0.75, are in continuous form. The upper and lower limits of the first class are 0.25 and 0 respectively. Hence, the class size is

(v) The given classes are 5-5.01, 5.01-5.02, 5.02-5.03, are in continuous form. The upper and lower limits of the first class are 5.01 and 5 respectively. Hence, the class size is

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) The frequency distribution table of grouped frequency such as 30-39, 40-49… is the following:

(ii) The highest score is 100.

(iii) The lowest score is 37.

(iv) The range of the scores is

(v) If 40 is the pass mark, then the number of students failed is 2.

(vi) The number of students scored more than 75 is 8.

(vii) The observations 51, 54 and 57 in between 50-60 have not actually appeared.

(viii) Number of students scored less than 50 is 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 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?

Answer 10:

(i) The weights of the new born babies (in kg) in descending order are

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

(ii) The highest weight is 3.1 kg.

(iii) The lowest weight is 2.1 kg.

(iv) The range of the weights is

(v) On that day, the number of babies born is 15.

(vi) Number of babies’ of weight less than 2.5 kg is 4.

(vii) Number of babies’ of weight more than 2.8 kg is 4.

(viii) Number of babies’ of weight 2.8 kg is 2.

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Question 11:

The number of runs scored by a cricket player in 25 innings are as follows:
26, 35, 94, 48, 82, 105, 53, 0, 39, 42, 71, 0, 64, 15, 34, 67, 0, 42, 124, 84, 54, 48, 139, 64, 47

(a) Rearrange these runs in ascending order.

(b) Determine the player, is highest score.

(c) How many times did the player not score a run?

(d) How many centuries did he score?

(e) How many times did he score more than 50 runs?

Answer 11:

(i) After arranging in ascending order, the given data (runs) is 0, 0, 0, 15, 26, 34, 35, 39, 42, 42, 47, 48, 48, 53, 54, 64, 64, 67, 71, 82, 84, 94, 105, 124 and 139.

(ii) The highest score of the player is 139.

(iii) The player did not score any run 3 times.

(iv) He scored 3 centuries.

(v) He scored more than 50 runs 12 times.

Question 12:

The class size of a distribution is 25 and the first class-interval is 200-224. There are seven class-intervals.

(i) Write the class-intervals.

(ii) Write the class-marks of each intervals.

Answer 12:

Since, there are 7 class intervals and first class is 200–224, therefore all the class intervals are:

(i) 200–224

(ii) 225–249

(iii) 250–274

(iv)275–299

(v)300–324

(vi)325–349

(viii)350–374

We know that the class mark corresponding to each class mark is given by:

Now,

Therefore, the class marks are:

212, 237, 262, 287, 312, 337 and 362

Question 13:

Write the class size and class limits in each of the following:

(i) 104, 114, 124, 134, 144, 154 and 164

(ii) 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97 and 102

(iii) 12.5, 17.5, 22.5, 27.5, 32.5, 37.5, 42.5, 47.5

 

Answer 13:

(i) Here, the data is distributed uniformly. So the class size h is given by difference between any two consecutive data. So,

If a is the class mark of a class interval and h be the class size, then the lower and upper limits of the class interval are: respectively

Lower limit of first class interval is;

And, upper limit of first class interval is:

Other class limits are:

(ii) Here, the data is distributed uniformly. So the class size h is given by difference between any two consecutive data. So,

If a is the class mark of a class interval and h be the class size, then the lower and upper limits of the class interval are: respectively

Lower limit of first class interval is;

And, upper limit of first class interval is:

Other class limits are:

(iii) Here, the data is distributed uniformly. So the class size h is given by difference between any two consecutive data. So,

If a is the class mark of a class interval and h be the class size, then the lower and upper limits of the class interval are: respectively

Lower limit of first class interval is;

And, upper limit of first class interval is:

Other class limits are:

Question 14:

Following data gives the number of children in 40 families:
1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 0, 4, 4, 3, 2, 2, 0, 0, 1, 2, 2, 4, 3, 2, 1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2, 2.

Represent it in the form of a frequency distribution.

Answer 14:

Here, the maximum and minimum values of the variate are 6 and 0 respectively.

So the range = 6 – 0 = 6

Here, we will take class size 1. So we must have 6 classes each of size 1.

Therefore, the frequency distribution in which the lower limit is included and upper limit excluded is:

Question 15:

The marks scored by 40 students of class IX in mathematics are given below:
81, 55, 68, 79, 85, 43, 29, 68, 54, 73, 47, 35, 72, 64, 95, 44, 50, 77, 64, 35, 79, 52, 45, 54, 70, 83, 62, 64, 72, 92, 84, 76, 63, 43, 54, 38, 73, 68, 52, 54

Prepare a frequency distribution with class size of 10 marks.

Answer 15:

Here, the maximum and minimum values of the variate are 95 and 29 respectively.

So the range = 95 – 29 = 66

Here, we will take class size 10. So we must have 7 classes each of size 10

Lower limit of first class interval is;

And, upper limit of first class interval is:

Therefore, the frequency distribution in which the lower limit is included and upper limit excluded is:

Question 16:

The heights (in cm) of 30 students of class IX are given below:
155, 158, 154, 158, 160, 148, 149, 150, 153, 159, 161, 148, 157, 153, 157, 162, 159, 151, 154, 156, 152, 156, 160, 152, 147, 155, 163, 155, 157, 153

Prepare a frequency distribution table with 160-164 as one of the class intervals.

Answer 16:

One of the class intervals is 160–164. This means that class size is 4

Here, the maximum and minimum values of the variate are 163 and 147 respectively.

So the range = 163 – 147 = 16

Here, we will take class size 4. So we must have 5 classes each of size 4

Lower limit of first class interval is;

And, upper limit of first class interval is:

Therefore, the frequency distribution in which the lower limit is included and upper limit excluded is:

Question 17:

The monthly wages of 30 workers in a factory are given below:

83.0, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 836, 878, 840, 868, 890, 806, 840, 890.

Represent the data in the form of a frequency distribution with class size 10.

Answer 17:

Here, the maximum and minimum values of the variate are 898 and 804 respectively.

So the range = 898 – 804 = 94

Here, we will take class size 10. So we must have 94/10 i.e. 10 classes each of size 10.

Therefore, the frequency distribution in which the lower limit is included and upper limit excluded is:

Lower limit of first class interval is;

And, upper limit of first class interval is:

Other class limits are:

Question 18:

The daily maximum temperatures (in degree celsius) recorded in  a certain city during the month of November are as follows:

25.8, 24.5, 25.6, 20.7, 21.8, 20.5, 20.6, 20.9, 22.3, 22.7, 23.1, 22.8, 22.9, 21.7, 21.3, 20.5, 20.9, 23.1, 22.4, 21.5, 22.7, 22.8, 22.0, 23.9, 24.7, 22.8, 23.8, 24.6, 23.9, 21.1

Represent them as a frequency distribution table with class size 1°C.

Answer 18:

Here, the maximum and minimum values of the variate are 25.8 and 20.5 respectively.

So the range = 25.8 – 20.5 = 5.3

Here, we will take class size 1.

Lower limit of first class interval is;

And, upper limit of first class interval is:

Therefore, the frequency distribution in which the lower limit is included and upper limit excluded is:

Question 19:

Construct a frequency table with equal class intervals from the following data on the monthly wages (in rupees) of 28 labourers working in a factory, taking one of the class intervals as 210-230 (230 not included):

220, 268, 258, 242, 210, 268, 272, 242, 311, 290, 300, 320, 319, 304, 302, 318, 306, 292, 254, 278, 210, 240, 280, 316, 306, 215, 256, 236.

Answer 19:

Here, the maximum and minimum values of the variate are 320 and 210 respectively.

So the range = 320 – 210 = 110

Here, we will take class size 20 (As one class interval is 210–230).

Therefore, the frequency distribution in which the lower limit is included and upper limit excluded is:

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Question 20:

The blood groups of 30 students of class VIII are recorded as follows:
A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O,
A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O

Represent this data in the form of a frequency distribution table. Find out which is the most common and which is the rarest blood group among these students.

Answer 20:

It can be observed that 9 students have their blood group as A, 6 as B, 3 as AB, and 12 as O.

Therefore, the blood group of 30 students of the class can be represented as follows.

Blood group

Number of students

A

9

B

6

AB

3

O

12

Total

30

It can be observed clearly that the most common blood group and the rarest blood group among these students is O and AB respectively as 12 (maximum number of students) have their blood group as O, and 3 (minimum number of students) have their blood group as AB.

Question 21:

Three coins were tossed 30 times. Each time the number of heads occurring was noted down as follow:
 

0 1 2 2 1 2 3 1 3 0
1 3 1 1 2 2 0 1 2 1
3 0 0 1 1 2 3 2 2 0

Prepare a frequency distribution table for the data given above.

Answer 21:

By observing the data given above, the required frequency distribution table can be constructed as follows.

Number of heads

Number of times (frequency)

0

6

1

10

2

9

3

5

Total 

30

Question 22:

Thirty children were asked about the number of hours they watched T.V. programmes in the previous week. The results were found as follows:
 

1 6 2 3 5 12 5 8 4 8
10 3 4 12 2 8 15 1 17 6
3 2 8 5 9 6 8 7 14 12

(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5-10.

(ii) How many children watched television for 15 or more hours  a week?

Answer 22:

(i) Our class intervals will be 0 − 5, 5 − 10, 10 −15…..

The grouped frequency distribution table can be constructed as follows.

Hours 

Number of children

0 − 5

10

5 − 10

13

10 − 15

5

15 − 20

2

Total 

30

(ii) The number of children who watched TV for 15 or more hours a week is 2 (i.e., the number of children in class interval 15 − 20).

Question 23:

The daily minimum temperatures in degrees Celsius recorded in a certain Arctic region are as follows:

− 12.5, −10.8, −18.6, −8.4, −10.8, −4.2, −4.8, −6.7, −13.2, −11.8, −2.3, 1.2, 2.6, 0, −2.4, 0, 3.2, 2.7, 3.4, 0, −2.4, −2.4, 0, 3.2, 2.7, 3.4, 0, −2.4, −5.8, −8.9, −14.6, −12.3, −11.5, −7.8, −2.9.

Represent them as frequency distribution table taking −19.9 to − 15 as the first class interval.

Answer 23:

Since the first class is –19.9 to –15

Therefore, the frequency distribution in which the lower limit is included and upper limit excluded is:

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