GSEB Class 9 Maths Solutions Chapter 14 Statistics Exercise 14.2

 

Question 1. The blood groups of 30 students of class 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? [NCERT Exemplar]
Answer:

O represents the most frequently appearing blood group, while AB is the least common type among these learners.
In simple words: The table shows how many students have each blood group. Blood group O is the most common, and blood group AB is the rarest.

Exam Tip: When constructing a frequency distribution table, ensure accurate tally marks and sum the frequencies to match the total number of observations.

 

Question 2. The distance (in km) of 40 engineers from their residence to their place of work was 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?
Answer:

We notice the following points from this table:
1. The travel distance (in kilometers) from home to work for the majority of engineers is under 20 km.
2. A very small number of engineers reside 20 km or more from their job location.
In simple words: Most engineers live less than 20 km from work, and only a few live 20 km or further.

Exam Tip: When making a grouped frequency table, be careful with class intervals. Ensure that the upper limit of one class doesn't overlap with the lower limit of the next, unless specified (e.g., exclusive intervals).

 

Question 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?
Answer:
(i)

(ii) This information seems to be gathered during the monsoon season since the relative humidity levels are quite high.
(iii) To find the range, we subtract the lowest value from the highest value. This gives us \( 99.2 - 84.9 = 14.3 \) percent.
In simple words: The table groups humidity levels. High humidity suggests it's the rainy season. The range shows the difference between the highest and lowest humidity readings.

Exam Tip: When identifying a season from humidity data, remember that high relative humidity typically indicates a rainy or monsoon period, while low humidity suggests dry weather.

 

Question 4. The heights of 50 students, measured to the nearest centimetres, 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?
Answer:
(i)

(ii) The majority of students have heights between 160-165 cm, while the fewest students are in the 170-175 cm group. Over half of all students are shorter than 165 cm.
In simple words: Most students are between 160-165 cm tall, with very few being 170-175 cm. More than half the students are shorter than 165 cm.

Exam Tip: Always double-check your tally marks against the raw data to avoid errors in frequency counts. Ensure your conclusions are directly supported by the data in your table.

 

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
0.08 0.01 0.10 0.06
0.11 0.07 0.05
(i) Make a grouped frequency distribution table for this data with class intervals as 0.00-0.04, 0.04-0.08, as so on.
(ii) For how many days, was the concentration of sulphur dioxide more than 0.11 parts per million?
Answer:
(i)

(ii) The amount of sulphur dioxide in the air was greater than 0.11 parts per million for \( 2 + 4 + 2 = 8 \) days.
In simple words: The table shows how often certain levels of sulphur dioxide were found. Adding up the days for levels above 0.11 ppm gives us 8 days.

Exam Tip: When dealing with continuous data, be careful to define your class intervals clearly (e.g., 0.00-0.04 means 0.00 to less than 0.04). Also, ensure you include all data points accurately in your tallies.

 

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:

In simple words: This table shows how often each number of heads (0, 1, 2, or 3) appeared when three coins were tossed 30 times.

Exam Tip: For tally marks, remember to cross out every fifth mark to group them efficiently. This helps prevent counting errors and makes the table easier to read.

 

Question 7. The value of it up to 50 decimal places is given below: 3.1415926535897932384626433832795028841 9716939937510.
(i) Make a frequency distribution of the digits from O to 9 after the decimal point.
(ii) What are the most and the least frequency occurring digits?
Answer:
(i)

(ii) The numbers that appear most often are 3 and 9. The digit that shows up the least frequently is 0.
In simple words: We counted how many times each digit from 0 to 9 appeared after the decimal point in the given number. Digits 3 and 9 showed up the most, while 0 appeared the least.

Exam Tip: When making a frequency distribution for digits in a long number, be extremely careful in counting each occurrence. A small mistake can alter the entire frequency table and subsequent conclusions.

 

Question 8. Thirty children were asked about the number of hours they watched TV programmes in the previous week. The result was 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:
(i)

(ii) According to the table, 2 children viewed television for 15 or more hours each week.
In simple words: The table groups how many hours children watched TV. Only 2 children watched TV for 15 or more hours.

Exam Tip: When asked to count items within a certain range from a frequency table, make sure to consider all appropriate class intervals. For "15 or more hours", include the class that starts at 15 and any classes above it.

 

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 table for this data, using class intervals of size 0.5 starting from the interval 2-2.5.
Answer:

In simple words: This table shows how long car batteries lasted in years, grouped into intervals. Most batteries lasted between 3.0 and 3.5 years.

Exam Tip: For continuous data, ensure that the upper boundary of a class interval is not included in that class but in the next (e.g., 2.0-2.5 includes values up to, but not including, 2.5). This prevents any data points from being counted twice or missed.