Maharashtra Board Class 8 Maths Chapter 11 Statistics Set 11.1 Solutions

Statistics Class 8 Maths Chapter 11 Practice Set 11.1 Solutions Maharashtra Board

Std 8 Maths Practice Set 11.1 Chapter 11 Solutions Answers

Question 1. The following table shows the number of saplings planted by 30 students. Fill in the boxes and find the average number of saplings planted by each student.

No. of saplings (Scores) \(x_i\)	No. of students (frequency) \(f_i\)	\(f_i \times x_i\)
1	4	4
2	6	-
3	12	-
4	8	-
N = _		\( \Sigma f_i \times x_i = \text{_} \)

Mean \( \bar{x} = \frac{\text{_}}{\text{N}} \)
Mean \( \bar{x} = \frac{\text{_}}{\text{_}} \)
Mean \( \bar{x} = \text{_} \)
.. The average number of trees planted is
Answer: Solution:

No. of saplings (Scores) \(x_i\)	No. of students (frequency) \(f_i\)	\(f_i \times x_i\)
1	4	4
2	6	12
3	12	36
4	8	32
N = 30		\( \Sigma f_i \times x_i = 84 \)

Mean \( \bar{x} = \frac{\Sigma f_i x_i}{N} \)
Mean \( \bar{x} = \frac{84}{30} = \frac{14 \times 6}{5 \times 6} = \frac{14}{5} \)
Mean \( \bar{x} = 2.8 \)
.. The average number of trees planted is 2.8.
In simple words: To find the average, we multiply the number of saplings by the number of students for each category, sum these products, and then divide by the total number of students. This gives us the mean number of saplings per student.

🎯 Exam Tip: Remember to clearly show all steps of calculating \(f_i \times x_i\) for each row and the final summation. Pay attention to accurate division for the mean.

 

Question 2. The following table shows the electricity (in units) used by 25 families of Eklara village in a month of May. Complete the table and answer the following questions.

Electricity used (Units) \(x_i\)	No. of families (frequency) \(f_i\)	\(f_i \times x_i\)
30	4
45	6
60	12
75	8
90	3
N = _		\( \Sigma f_i \times x_i = \text{_} \)

(i) How many families use 45 units electricity?
(ii) State the score, the frequency of which is 5.
(iii) Find N, and \( \Sigma f_i \times x_i \).
(iv) Find the mean of electricity used by each family in the month of May.
Answer: Solution:

Electricity used (Units) \(x_i\)	No. of families (frequency) \(f_i\)	\(f_i \times x_i\)
30	7	210
45	2	90
60	8	480
75	5	375
90	3	270
N = 25		\( \Sigma f_i \times x_i = 1425 \)

(i) 2 families used 45 units of electricity.
(ii) The score for which the frequency is 5 is 75.
(iii) N = 25 and \( \Sigma f_i \times x_i = 1425 \).
(iv) Mean \( (\bar{x}) = \frac{\Sigma f_i x_i}{N} \)
\( = \frac{1425}{25} \)
Mean \( (\bar{x}) = 57 \) The mean of electricity used by each family is 57 units.
In simple words: We completed the frequency table by calculating the product of electricity units and the number of families. Then, we found N (total families) and the sum of all \(f_i x_i\) values. Finally, the mean was calculated by dividing this sum by N.

🎯 Exam Tip: Ensure precise multiplication for each \(f_i \times x_i\) entry. When answering sub-questions, extract information directly from the completed frequency table for accuracy.

 

Question 3. The number of members in the 40 families in Bhilar are as follows: 1, 6, 5, 4, 3, 2, 7, 2, 3, 4, 5, 6, 4, 6, 2, 3, 2, 1, 4, 5, 6, 7, 3, 4, 5, 2, 4, 3, 2, 3, 5, 5, 4, 6, 2,3, 5, 6, 4, 2. Prepare a frequency table and And the mean of members of 40 families.
Answer: Solution:

Number of members (\(x_i\))	Tally marks	No. of families (frequency) \(f_i\)	\(f_i \times x_i\)
1	||	2	2
2	NIII	8	16
3	NII	7	21
4	NII	8	32
5	NII	7	35
6	NI	6	36
7	||	2	14
	N = 40		\( \Sigma f_i x_i = 156 \)

Mean \( (\bar{x}) = \frac{\Sigma f_i x_i}{N} \)
\( = \frac{156}{40} = \frac{39 \times 4}{10 \times 4} = \frac{39}{10} \)
.. \( \bar{x} = 3.9 \)
.. The mean of the members of 40 families is 3.9.
In simple words: First, we organized the raw data into a frequency table using tally marks to count the occurrences of each number of family members. Then, we calculated \(f_i x_i\) for each row and summed them up to find \( \Sigma f_i x_i \). Finally, we divided this sum by the total number of families (N) to get the mean.

🎯 Exam Tip: Be careful while counting tally marks to ensure the frequency for each category is accurate. Double-check your summation of \(f_i x_i\) and the final division for the mean.

 

Question 4. The number of Science and Mathematics projects submitted by Model high school, Nandpur in last 20 years at the state level science exhibition is: 2, 3,4, 1, 2, 3, 1, 5, 4, 2, 3, 1, 3, 5, 4, 3, 2, 2, 3, 2. Prepare a frequency table and find the mean of the data.
Answer: Solution:

Number of projects (\(x_i\))	Tally marks	No. of years (frequency) \(f_i\)	\(f_i \times x_i\)
1	III	3	3
2	NI	6	12
3	ZI	6	18
4	III	3	12
5	||	2	10
	N = 20		\( \Sigma f_i x_i = 55 \)

Mean \( (\bar{x}) = \frac{\Sigma f_i x_i}{N} \)
\( = \frac{55}{20} = \frac{11 \times 5}{4 \times 5} = \frac{11}{4} \)
.. Mean \( (\bar{x}) = 2.75 \)
.. The mean of the given data is 2.75.
In simple words: We created a frequency table from the given project submission data, counting how many years had 1, 2, 3, 4, or 5 projects. We then calculated the product of projects and frequency for each category, summed these products, and divided by the total number of years (N) to find the mean.

🎯 Exam Tip: Accuracy in constructing the frequency table from the raw data is crucial. Ensure correct tallying and subsequent calculations for \(f_i x_i\) and the mean.

Maharashtra Board Class 8 Maths Chapter 11 Statistics Practice Set 11.1 Intext Questions And Activities

 

Question 1. The number of pages of a book Ninad read for five consecutive days were 60, 50, 54, 46, 50. Find the average number of pages he read everyday. (Textbook pg. no. 67)
Answer: Solution: \( \frac{60+50+54+46+50}{5} = \frac{260}{5} = 52 \)
.. Average number of pages read daily is 52.
In simple words: To find the average number of pages, we sum the total pages read over five days and divide by the number of days, which is five.

🎯 Exam Tip: For simple average calculations, ensure all values are correctly summed, and the division is by the exact count of observations.

Std 8 Maths Digest

• Practice Set 11.1 Class 8 Answers
• Practice Set 11.2 Class 8 Answers
• Practice Set 11.3 Class 8 Answers
• Practice Set 12.1 Class 8 Answers
• Practice Set 12.2 Class 8 Answers
• Practice Set 13.1 Class 8 Answers
• Practice Set 13.2 Class 8 Answers
• Practice Set 14.1 Class 8 Answers
• Practice Set 14.2 Class 8 Answers