AP State Syllabus AP Board 7th Class Maths Solutions Chapter 7 Data Handling Ex 3 Textbook Questions and Answers.
AP State Syllabus 7th Class Maths Solutions 7th Lesson Data Handling Exercise 3
Question 1.
Say true or false and why?
(i) The difference between the largest and smallest observations in a data set is called the
mean.
(ii) In a bar graph, the bar which has greater length indicates mode.
(iii) Value of every observation in the data set is taken into account when median is calculated.
(iv) The median of a set of numbers is always one of the numbers
Solution:
i) False
ii) True
iii) False.
We take only the mid value when the observations are arranged either in ascending / descending order.
iv) False
It may or may not be in the data set.
Question 2.
The monthly income (in rupees) of 7 households in a village are 1200, 1500, 1400, 1000, 1000, 1600, 10000. (i) Find the median income of the house holds. (ii) If one more household with monthly income of 1500 is added, what will the median income be?
Solution:
Given that
The household incomes in Rs. are 1200, 1500. 1400, 1000, 1000, 1600, 10,000
Arranging these observations in ascending order 1000, 1000, 1200, 1400, 1500, 1600, 10,000
Medían is the mid value = Rs. 1400
If one more household with income Rs. 1500 ¡s added them the data becomes
1000, 1000, 1200. 1400, 1500, 1500, 1600, 10,000
Now the median = average of 1400 and 1500
= \(\frac{1400+1500}{2}=\frac{2900}{2}\) = Rs.1450
Question 3.
Observations of a data are 16, 72,0, 55, 65, 55, 10, and 41. Chaitanya calculated the mode and median without taking the zero into consideration. Did Chaitanya do the right thing?
Solution:
Mode is correct but median is wrong.
Question 4.
How many distinct sets of three positive integers have a mean of 6, a median of 7, and no mode?
Solution:
It is not possible
Question 5.
Four integers arc added to a group of integers 3,4,5,5 and 8 and the mean, median, and mode of the data increases by 1 each. What is the greatest integer in the new group of integers?
Solution:
Given set of integers = 3, 4, 5, 5 and 8
The mean of the given data = \(\frac{\text { Sum of the integers }}{\text { Number of integers }}=\frac{3+4+5+5+8}{5}=\frac{25}{5}\) = 5
The median of the given data 3. 4. 5, 5. 8 (already in ascending order) = 5 (the mid
Mode of the given data 3. 4. 5. 58 iS 5.
After adding 4 integers the mean, mode and median increased by 1
New
Mean = 5 + 1 = 6
Median = 5 + 1 = 6
Mode = 5 + 1 = 6
Now sum of the (5 + 4 = 9) numbers = Number of integers × average
Sum = 9 × 6 = 54
But sum of the given set of 5 numbers = 25
∴ Sum of the newly added 4 numbers = 54 – 25 = 29
Mode = 6 means 6 should appear for 3 times.
But sum of four numbers = 29
29 = 6 + 6 + 6 + fourth number
29 = 18 + fourth number
∴ fourth number = 29 – 18 = 11