Access Answers for SAT Maths Chapter 14 – Statistics
Exercise 14.1
1. Give five examples of data that you can collect from your day-to-day life.
Solution:
Five examples from day-to-day life:
1. Number of students in our class.
2. Number of fans in our school.
3. Electricity bills of our house for last two years.
4. Election results obtained from television or newspapers.
5. Literacy rate figures obtained from Educational Survey
2. Classify the data in Q.1 above as primary or secondary data.
Solution:
Primary data: when the information was collected by the investigator herself or himself with a
definite objective in her or his mind, the data obtained is called primary data.
Primary data; (i), (ii) and (iii)
Secondary data; when the information was gathered from a source which already had the
information stored, the data obtained is called secondary data
Secondary data; (iv) and (v)
Exercise 14.2
1. 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. Which is the most common, and
which is the rarest, blood group among these students?
Solution:
Frequency is the number of students having the same blood group. The frequency is represented in
the table or the frequency distribution table:
Blood Group Number of Students
(Frequency)
A 9
B 6
O 12
, AB 3
Total 30
The most common Blood Group is the blood group with highest frequency: O
The rarest Blood Group is the blood group with lowest frequency: AB
2. The distance (in km) of 40 engineers from their residence to their place of work were found as
follows:
5 3 10 20 25 11 13 7 12 31
19 10 12 17 18 11 32 17 16 2
7 9 7 8 3 5 12 15 18 3
12 14 2 9 6 15 15 7 6 12
Construct a grouped frequency distribution table with class size 5 for the data given above taking
the first interval as 0-5 (5 not included). What main features do you observe from this tabular
representation?
Solution:
Since the given data is very large, we construct a grouped frequency distribution table of class size
5. ∴, class interval will be 0-5, 5-10, 10-15, 15-20 and so on. The data is represented in the grouped
frequency distribution table as:
In the given table the classes do not overlap. Also we find that, the houses of 36 out of 40 engineers
are below 20 km of distance
3. The relative humidity (in %) of a certain city for a month of 30 days was as follows:
98.1 98.6 99.2 90.3 86.5 95.3 92.9 96.3 94.2 95.1
89.2 92.3 97.1 93.5 92.7 95.1 97.2 93.3 95.2 97.3
96.2 92.1 84.9 90.2 95.7 98.3 97.3 96.1 92.1 89
(i) Construct a grouped frequency distribution table with classes 84 – 86, 86 – 88, etc.
(ii) Which month or season do you think this data is about?
(iii) What is the range of this data?
Solution:
, (i) Since the given data is very large, we construct a grouped frequency distribution table of class
size 2.
∴, class interval will be 84-86, 86-88, 88-90, 90-92 and so on. The data is represented in the grouped
frequency distribution table as:
Relative humidity (in %) Frequency
84-86 1
86-88 1
88-90 2
90-92 2
92-94 7
94-96 6
96-98 7
98-100 4
Total 30
(ii) The humidity is very high in the given data. Since the humidity is observed to be high during the
rainy season, the data here must be about rainy season.
(iii) The range of a data = The maximum value of the data–minimum value of the data
= 99.2−84.9
= 14.3
4. The heights of 50 students, measured to the nearest centimeters, have been found to be as
follows:
161 150 154 165 168 161 154 162 150 151
162 164 171 165 158 154 156 172 160 170
153 159 161 170 162 165 166 168 165 164
154 152 153 156 158 162 160 161 173 166
161 159 162 167 168 159 158 153 154 159
(i) Represent the data given above by a grouped frequency distribution table, taking the class
intervals as 160 – 165, 165 – 170, etc.
(ii) What can you conclude about their heights from the table?
Solution:
(i) The data given in the question can be represented by a grouped frequency distribution table,
taking the class intervals as 160 – 165, 165 – 170, etc., as:
Height (in cm) No. of Students
Exercise 14.1
1. Give five examples of data that you can collect from your day-to-day life.
Solution:
Five examples from day-to-day life:
1. Number of students in our class.
2. Number of fans in our school.
3. Electricity bills of our house for last two years.
4. Election results obtained from television or newspapers.
5. Literacy rate figures obtained from Educational Survey
2. Classify the data in Q.1 above as primary or secondary data.
Solution:
Primary data: when the information was collected by the investigator herself or himself with a
definite objective in her or his mind, the data obtained is called primary data.
Primary data; (i), (ii) and (iii)
Secondary data; when the information was gathered from a source which already had the
information stored, the data obtained is called secondary data
Secondary data; (iv) and (v)
Exercise 14.2
1. 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. Which is the most common, and
which is the rarest, blood group among these students?
Solution:
Frequency is the number of students having the same blood group. The frequency is represented in
the table or the frequency distribution table:
Blood Group Number of Students
(Frequency)
A 9
B 6
O 12
, AB 3
Total 30
The most common Blood Group is the blood group with highest frequency: O
The rarest Blood Group is the blood group with lowest frequency: AB
2. The distance (in km) of 40 engineers from their residence to their place of work were found as
follows:
5 3 10 20 25 11 13 7 12 31
19 10 12 17 18 11 32 17 16 2
7 9 7 8 3 5 12 15 18 3
12 14 2 9 6 15 15 7 6 12
Construct a grouped frequency distribution table with class size 5 for the data given above taking
the first interval as 0-5 (5 not included). What main features do you observe from this tabular
representation?
Solution:
Since the given data is very large, we construct a grouped frequency distribution table of class size
5. ∴, class interval will be 0-5, 5-10, 10-15, 15-20 and so on. The data is represented in the grouped
frequency distribution table as:
In the given table the classes do not overlap. Also we find that, the houses of 36 out of 40 engineers
are below 20 km of distance
3. The relative humidity (in %) of a certain city for a month of 30 days was as follows:
98.1 98.6 99.2 90.3 86.5 95.3 92.9 96.3 94.2 95.1
89.2 92.3 97.1 93.5 92.7 95.1 97.2 93.3 95.2 97.3
96.2 92.1 84.9 90.2 95.7 98.3 97.3 96.1 92.1 89
(i) Construct a grouped frequency distribution table with classes 84 – 86, 86 – 88, etc.
(ii) Which month or season do you think this data is about?
(iii) What is the range of this data?
Solution:
, (i) Since the given data is very large, we construct a grouped frequency distribution table of class
size 2.
∴, class interval will be 84-86, 86-88, 88-90, 90-92 and so on. The data is represented in the grouped
frequency distribution table as:
Relative humidity (in %) Frequency
84-86 1
86-88 1
88-90 2
90-92 2
92-94 7
94-96 6
96-98 7
98-100 4
Total 30
(ii) The humidity is very high in the given data. Since the humidity is observed to be high during the
rainy season, the data here must be about rainy season.
(iii) The range of a data = The maximum value of the data–minimum value of the data
= 99.2−84.9
= 14.3
4. The heights of 50 students, measured to the nearest centimeters, have been found to be as
follows:
161 150 154 165 168 161 154 162 150 151
162 164 171 165 158 154 156 172 160 170
153 159 161 170 162 165 166 168 165 164
154 152 153 156 158 162 160 161 173 166
161 159 162 167 168 159 158 153 154 159
(i) Represent the data given above by a grouped frequency distribution table, taking the class
intervals as 160 – 165, 165 – 170, etc.
(ii) What can you conclude about their heights from the table?
Solution:
(i) The data given in the question can be represented by a grouped frequency distribution table,
taking the class intervals as 160 – 165, 165 – 170, etc., as:
Height (in cm) No. of Students
