CBSE Class 9 Maths - CH14 - Statistics (NCERT Ex 14.1 and 14.2)
STATISTICS (NCERT EX 14.1 AND 14.2)
NCERT Exercise 14.1
Question:1
Give five examples of data that you can collect from day to day life.
Answer:
In our day to day life,we can collect the following data.
1. Numbers of girl students per class in a school.
2. Number of cars of different models in our colony.
3. Production of rice in last 20 years in our country.
4. Rainfall in our city in the last 10 years.
5. Scores made by a team in Indian Premier League tournament.
5. Scores made by a team in Indian Premier League tournament.
Question:2
Classify the data in Q1 above as primary or secondary data.
Answer:
The information which is collected by the investigator himself with defined objectives is called as primary data whereas when the information is gathered from a source which already had stored, is called as secondary data.
Item 1 and 2 are the primary data where as the data in 3, 4 and 5 is secondary data.
Item 1 and 2 are the primary data where as the data in 3, 4 and 5 is secondary data.
Exercise 14.2
Question: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 the data in frequency distribution table.which the most common,and which is the rarest,blood group among these students?
Answer:
It is observed that 9 students have their blood group as A,6 B,3 as AB and 12 as O.
Therefore,the blood group of 30 students represented as follows:
| Blood group | Number of students |
|---|---|
| A | 9 |
| B | 6 |
| AB | 3 |
| O | 12 |
It is clear seen 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 there blood group as O, and 3 (minimum number of students) have their blood group as AB.
Question:2
The relative humidity (in %) of a certain city for a month of 30 days was as follows:
98.1 98.6 99.2 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 as
(ii) Which month or season do you think this data is about?
(iii) What is the range of this data?
Answer:
(i) A grouped frequency distribution table of class size 2 needs to be constructed.
The class intervals will be 84-86, 86-88 and 88-90..
By observing the data given above, the required table is constructed as follows:
| Relative humidity(in %) | Number of days(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) It is seen that the relative humidity is high. Therefore, it is a month of rainy season
(iii) Range of data = maximum value - minimum value
= 99.2 - 84.3 = 14.3
Question:4
The heights of 50 students, measured to the nearest centimeters,
have been found as follows.
161 150 154 165 168 161 164 162 150 151
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 but their heights from the table?
Answer:
(i) A grouped frequency distribution table is to be constructed taking class intervals 160-165,165-170,etc.By observing the data given above, the required table can be constructed as follows.
| Height(in cm) | Number of students(frequency) |
|---|---|
| 150-155 | 12 |
| 155-160 | 9 |
| 160-165 | 14 |
| 165-170 | 10 |
| 170-175 | 5 |
| Total | 50 |
(ii) It is observed that more than 50% of the students are shorter than 165 cm.
Question:5
A study was conducted to find out the concentration of sulphur dioxide in the air in
parts per million (ppm) of a certain city. The data obtained for 30 days is as follows:
0.03 0.08 0.08 0.09 0.04 0.17
0.16 0.05 0.02 0.06 0.18 0.20
0.11 0.08 0.12 0.13 0.22 0.07
0.08 0.01 0.10 0.07 0.09 0.18
0.11 0.07 0.05 0.07 0.01 0.04
(i) Make a grouped frequency distribution table for this data with class intervals as
0.00 - 0.04, 0.04 - 0.08, and so on
(ii) For how many days, was the concentration af sulphur dioxide more than 0.11 patts per million?
Answer:
Taking class intervals as 0.00-0.04,0.04-0.08 and so on grouped frequency table is as follows:
| Concentration of SO2 | Number of days(frequency) |
|---|---|
| 0.00 - 0.04 | 4 |
| 0.04 - 0.08 | 9 |
| 0.08 - 0.12 | 9 |
| 0.12 - 0.16 | 2 |
| 0.16 - 0.20 | 4 |
| 0.20 - 0.24 | 2 |
| Total | 30 |
The number of days for which the concentration of SO2 is more than 0.11 is the number of days for which the concentration is in between 0.12 - 0.16, 0.16 - 0.20, 0.20 - 0.24
Required number of days = 2 + 4 + 2 = 8.
Therefore, for 8 days, the concentration of SO2 is more than 0.11 ppm.
Question 6:
Three coins were tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows.
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:
By observing the data given above, the required frequency distribution table can be constructed as follows.
| Number of heads | Number of items(frequency) |
|---|---|
| 0 | 6 |
| 1 | 10 |
| 2 | 9 |
| 3 | 5 |
| Total | 30 |
Question 7:
The value of pi upto 50 decimal places is given below:
3.14159265358979323846264338327950288419716939937510
(i) Make a frequency distribution of the digits from 0 to 9 after the decimal point.
(ii)What are the most and the leas frequently occurring digits?
Answer:
It observation of the digits after decimal point, the required table can be constructed as follows.
| Digit | Frequency |
|---|---|
| 0 | 2 |
| 1 | 5 |
| 2 | 5 |
| 3 | 8 |
| 4 | 4 |
| 5 | 5 |
| 6 | 4 |
| 7 | 4 |
| 8 | 5 |
| 9 | 8 |
| Total | 50 |
(ii) It is observed from the above table that the least frequency is 2 of digit O, and the maximum frequency is 8 of digit 3 and 9. Therefore, the most frequently occurring digits are 3 and 9 and the least frequently occurring digit is O
Question 8:
Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows:
1 6 2 3 5 1 2 5 8 4 8
1 0 3 4 1 1 7 6
3 2 8 5 9 6 8 7 1 4 1 2
(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 :
(i) Our class intervals will be O - 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 9:
A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:
2.6 3.0 3.7 3.2 2.2 4.1 3.5 4.5
3.5 2.3 3.2 3.4 3.8 3.2 4.6 3.7
2.5 4.4 3.4 3.3 2.9 3.0 4.3 2.8
3.5 3.2 3.9 3.2 3.2 3.1 3.7 3.4
4.6 3.8 3.2 2.6 3.5 4.2 2.9 3.6
Construct a grouped frequency distribution tab e for this data, size 0.5 starting from the intervals 2 - 2.5
Answer:
A grouped frequency table of class size 0.5 needs to be constructed, starting from class interval
2 - 2.5.
2 - 2.5.
Therefore, the class intervals will be 2 — 2.5, 2.5 — 3,3 3.5...
Observing the data given above, the required grouped frequency distribution table can be constructed as follows:
| Lives of batteries(in hours) | Number of batteries |
|---|---|
| 2 - 2.5 | 2 |
| 2.5 - 3.0 | 6 |
| 3.5 - 3.14 | 14 |
| 3.5 - 4.0 | 11 |
| 4.0 - 4.5 | 4 |
| 4.5 - 5.0 | 3 |
| Total | 40 |
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