RBSE Solutions Class 9 Maths Chapter 15 Statistics Exercise 15.2

Rajasthan Board RBSE Class 9 Maths Solutions Chapter 15 Statistics Ex 15.2

 

Question 1. The weight of 30 students (in kg) of Class X of a secondary school are as follows: 34, 34, 36, 37, 38, 33, 34, 35, 36, 37, 38, 33, 34, 35, 34, 33, 37, 35, 34, 36, 38, 36, 35, 34, 35, 37, 38, 34, 35, 35. Prepare a frequency table for it.
Answer: The frequency table for the given weights is prepared below:

In simple words: We list each unique weight and count how many times it appears in the given data. Tally marks help count these quickly. This helps organize the data clearly.

🎯 Exam Tip: Always double-check your tally marks and frequencies by summing them up to ensure they match the total number of data points given in the question.

 

Question 2. The weight (in kg) of 30 newly born babies in a village are as follows: 3.4, 3.6, 3.0, 3.8, 3.6, 3.8, 2.9, 3.4, 2.9, 3.4, 3.0, 3.4, 3.2, 3.1, 3.2, 3.2, 3.1, 3.2, 3.4, 3.0, 3.1, 3.2, 3.5, 3.7, 3.1, 3.0, 2.9, 3.0, 3.1, 3.2
Answer: The frequency table for the weights of the newly born babies is as follows:

In simple words: We listed all the different baby weights and then counted how many babies had each weight. This helps us see the distribution of weights.

🎯 Exam Tip: When creating a frequency table, ensure all unique data points are included, and the sum of frequencies matches the total number of observations.

 

Question 3. Three coins were tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows: 0, 0, 2, 2, 2, 1, 2, 2, 1, 3, 1, 1, 3, 1, 1, 3, 0, 0, 0, 1, 3, 0, 1, 2, 3, 1, 2, 3, 2, 3. Prepare a frequency distribution table for the these data.
Answer: We will count how many times each number of heads (0, 1, 2, or 3) appeared in the 30 tosses. This gives us the frequency distribution table:

In simple words: We recorded how many times 0, 1, 2, or 3 heads appeared when we tossed coins 30 times. This table shows how often each outcome happened.

🎯 Exam Tip: When counting frequencies for discrete data, like number of heads, list all possible outcomes (even if some have zero frequency) and ensure the total frequency matches the total number of trials.

 

Question 4. The blood groups of 30 students of Class X are recorded as follows: A, B, O, O, A, B, 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 these data in the form of a frequency distribution table. Which is the most common, and which is the rarest, blood group among these students?
Answer: First, we make a frequency distribution table to show how many students have each blood group:

From this table, we can see that blood group O has the highest frequency (12 students), making it the most common. Blood group AB has the lowest frequency (3 students), making it the rarest among these students.
In simple words: After counting, blood group O is found most often, and blood group AB is found least often.

🎯 Exam Tip: To find the most and least common items, simply look for the highest and lowest frequencies in your completed table.

 

Question 5. The marks obtained by 30 students of Class IX in an examination are as follows. Prepare a frequency table of 5 classes of class size 10. 19, 27, 40, 3, 33, 41, 18, 8, 20, 0, 23, 49, 16, 36, 14, 39, 6, 12, 29, 28, 22, 24, 37, 10, 23, 38, 35, 9, 49, 23
Answer: We need to prepare a frequency table with 5 classes, each with a size of 10. The maximum marks obtained are 49, and the minimum marks are 0. This means the range of marks is \( 49 - 0 = 49 \). Since the class size is 10, the number of intervals needed is \( \frac{49}{10} = 4.9 \), which we round up to 5 intervals to cover all data points. The classes will be 0-10, 10-20, 20-30, 30-40, and 40-50. Here is the frequency table:

In simple words: We organized the marks into groups of 10, like 0 to 9, 10 to 19, and so on. Then we counted how many students scored marks in each group.

🎯 Exam Tip: When forming class intervals for grouped frequency tables, always ensure that each data point falls into exactly one class, typically by excluding the upper boundary from the interval.

 

Question 6. Prepare a frequency table by taking 5 as width of the class interval from the following data 13, 11, 8, 19, 0, 44, 27, 10, 8, 35, 13, 27, 30, 17, 43, 23, 19, 43, 17, 7
Answer: To prepare the frequency table, we first find the maximum and minimum values in the data. The maximum value is 44, and the minimum value is 0. So, the range is \( 44 - 0 = 44 \). Given a class size of 5, we can determine the class intervals. We will start the first interval from 0 to include the minimum value. The class intervals will be: 0-5, 5-10, 10-15, 15-20, 20-25, 25-30, 30-35, 35-40, and 40-45.

In simple words: We grouped the given numbers into intervals of 5, then counted how many numbers fell into each group. This helps us see how the numbers are spread out.

🎯 Exam Tip: When the class size is given, carefully determine the class intervals, ensuring they are continuous and cover the full range of data, and remember to exclude the upper limit of each interval for counting.

 

Question 7. The value of \( \pi \) upto 50 decimal places is given below. 3.14159265358979323846264338327950288419716939937510
(i) Make a frequency distribution table of the digits from 0 to 9 after the decimal point.
(ii) What are the most and the least frequency occurring digits?
Answer:
(i) We extract the 50 digits after the decimal point from the value of \( \pi \) and count how many times each digit from 0 to 9 appears. This gives us the frequency distribution table:

(ii) From the table, we can see that the digits 3 and 9 both appear 8 times, making them the most frequently occurring digits. The digit 0 appears only 2 times, making it the least frequently occurring digit.
In simple words: We counted each digit from 0 to 9 after the decimal point in \( \pi \). Digits 3 and 9 show up the most often, while digit 0 shows up the least.

🎯 Exam Tip: When dealing with long sequences of digits, be very careful and systematic in counting each digit's frequency to avoid errors.

 

Question 8. The distance (in km) of 40 engineers from their residence to their place of work were. Make a grouped frequency distribution table for this data, taking a class size of 5. Take the first interval as 0 - 5 (5 not included). What main features do you observe from this tabular representation.
Answer: To create the grouped frequency table, we need to know the highest and lowest distances. The maximum distance is 32 km, and the minimum distance is 2 km. The range of distances is \( 32 - 2 = 30 \) km. Given that the class size is 5, and the first interval is 0-5 (excluding 5), the number of intervals will be \( \frac{30}{5} = 6 \). The class intervals will be: 0-5, 5-10, 10-15, 15-20, 20-25, 25-30, and 30-35. Here is the grouped frequency distribution table based on these calculations:

From this table, we observe that \( 5 + 11 + 11 + 9 = 36 \) engineers live up to 20 km from their work. This means only \( 1 + 1 + 2 = 4 \) engineers live at a distance of 20 km or more from their workplace. A large majority of engineers live relatively close to work.
In simple words: We grouped the engineers' distances into sets of 5 km. Most engineers live less than 20 km from work. Only a few live 20 km or further.

🎯 Exam Tip: When analyzing a grouped frequency table, pay attention to the cumulative frequencies to understand how many data points fall below or above certain values, which helps in drawing conclusions.

 

Question 9. Thirty children were asked about the number of hours they studied in the previous week. The results were found as follows: 2, 3, 5, 8, 6, 9, 8, 7, 14, 12, 6, 17, 1, 15, 8, 2, 12, 4, 3, 10, 3, 2, 6, 1, 12, 5, 8, 5, 8, 4
(i) Make a group frequency distribution table for these data, taking class width 5 and one of the class intervals as 5 - 10.
(ii) How many children studied for 15 or more hours in a week?
Answer:
(i) First, we find the maximum and minimum number of hours studied. The maximum hours studied is 17, and the minimum hours studied is 1. The range is \( 17 - 1 = 16 \). Given a class width of 5, and knowing that 5-10 is one of the intervals, we can set up the class intervals starting from 0 to cover the minimum value. The class intervals will be: 0-5, 5-10, 10-15, and 15-20. Here is the grouped frequency distribution table:

(ii) From the frequency table, the number of children who studied for 15 or more hours in a week falls into the 15-20 class interval. There are 3 children in this category.
In simple words: We organized the study hours into groups of 5 hours. (i) The table shows how many children studied for each range of hours. (ii) Three children studied for 15 hours or more.

🎯 Exam Tip: When answering questions about "X or more" from a grouped frequency table, add the frequencies of all class intervals that meet or exceed X.