SCERT AP 7th Class Maths Solutions Pdf Chapter 6 Data Handling Ex 6.1 Textbook Exercise Questions and Answers.
AP State Syllabus 7th Class Maths Solutions 6th Lesson Data Handling Ex 6.1
Question 1.
Find Arithmetic Mean of the following.
(i) 4, 5, 11, 8
Answer:
Given data: 4,5, 11, 8.
Sum of observations = 4 + 5 + 11 + 8 = 28
Number of observations = 4
∴ Arithmetic Mean = \(\frac{\text { Sum of observations }}{\text { Number of observations }}\) = \(\frac{28}{4}\) = 7.
(ii) 10, 15, 21, 12, 17
Answer:
Given data: 10, 15, 21, 12, 17
Sum of observations 10 + 15 + 21 + 12 + 17 = 75
Number of observations = 5
∴ Arithmetic Mean = \(\frac{\text { Sum of observations }}{\text { Number of observations }}\) = \(\frac{75}{5}\) = 15
(iii) \(\frac{1}{4}, \frac{1}{2}, \frac{3}{4}, \frac{3}{2}, \frac{5}{4}\)
Answer:
Given data: \(\frac{1}{4}, \frac{1}{2}, \frac{3}{4}, \frac{3}{2}, \frac{5}{4}\)
Sum of observations = \(\frac{1}{4}+\frac{1}{2}+\frac{3}{4}+\frac{3}{2}+\frac{5}{4}\) = \(\frac{1+2+3+6+5}{4}\) = \(\frac{17}{4}\)
Number of observations = 5
∴ Arithmetic Mean = \(\frac{\text { Sum of observations }}{\text { Number of observations }}\)
= \(\frac{\frac{17}{4}}{5}=\frac{17}{4} \div \frac{5}{1}=\frac{17}{4} \times \frac{1}{5}=\frac{17}{20}\)
∴ Arithmetic Mean = \(\frac{17}{20}\)
Question 2.
Amounts donated by eight students to ‘NIVAR’ cyclone effected people are ₹300, ₹450, ₹700, ₹650, ₹400, ₹750, ₹900 and ₹850. Find the Arithmetic Mean of amounts donated.
Answer:
Given data, ₹300, ₹450, ₹700, ₹650, ₹400, ₹750, ₹900 and ₹850.
Sum of observations = 300 + 450 + 700 +650 +400 + 750 + 900 + 850 = 5000
Number of observations = 8
∴ Arithmetic Mean = \(\frac{\text { Sum of observations }}{\text { Number of observations }}\) = \(\frac{5000}{8}\) = ₹625
∴ Arithmetic Mean of amount donated = ₹625
Question 3.
The number of passengers who travelled in APSRTC bus from Eluru to Rangapuram in 5 trips in a day are 35, 42, 28, 41 and 44. What is the average of number of passengers travelled per trip ?
Answer:
Given data are 35, 42, 28, 41, 44.
Sum of observations = 35 + 42 + 28 + 41 + 44 = 190
Number of observations = 5
∴ Arithmetic Mean (or) Average = \(\frac{\text { Sum of observations }}{\text { Number of observations }}\) = \(\frac{190}{5}\) = 38
∴Average of number of passengers travelled per trip = 38.
Question 4.
Find Arithmetic mean of factors of 24.
Answer:
Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
Sum of (factors) observations = 1 + 2 + 3 + 4 + 6 + 8+ 12 + 24 = 60
Number of observations = 8
∴ Arithmetic Mean = \(\frac{\text { Sum of observations }}{\text { Number of observations }}\) = \(\frac{60}{8}\) = 7.5
∴ Arithmetic Mean of factors of 24 is 7.5
Question 5.
Find the Arithmetic Mean of x, x + 1 and x + 2.
Answer:
Given data x, x + 1, x + 2.
Sum of observations = x + x + 1 + x + 2 = 3x + 3
Number of observations = 3
∴ Arithmetic Mean = \(\frac{\text { Sum of observations }}{\text { Number of observations }}\)
= \(\frac{3 x+3}{3}\) = \(\frac{3(x+1)}{3}\)
∴ Arithmetic mean = x + 1