Get the simplified Class 7 Maths Extra Questions and Class 7 Maths Part 2 Chapter 5 Connecting the Dots Extra Questions and Answers with complete explanation.
Class 7 Connecting the Dots Extra Questions
Connecting the Dots Extra Questions Class 7
Connecting the Dots Class 7 Very Short Question Answer
Question 1.
The heights of some children in a group are 152 cm, 166 cm, 164 cm, 158 cm, 156 cm, 170 cm. Find the mean height.
Solution :
Total number of given heights = 6 Sum of given heights = 152 + 166 + 164 + 158 + 156 + 170 = 966 cm
= \(\frac{966}{6}\) = 161 cm
Hence, the mean height is 161 cm.
Question 2.
The weights (in kg) of 9 students in a class are 42, 45, 38, 49, 52, 40, 44, 50 and 48. Find the median weight.
Solution :
Arranging the weights in ascending order 38, 40, 42, 44, 45, 48, 49, 50, 52 Since there are 9 values (an odd number), the middle value is the (\(\frac{9+1}{2}\)) termi.e., 5th term. So, median weight = 45 kg.
Question 3.
Determine the ‘k’ value if the arithmetic mean of 9,8,10, k, 12 is 15.
Solution :
\(\frac{9+8+10+k+12}{5}\) = 15
39 + k = 75
k = 75-39
k = 36
Hence, the value of k is 36.
Question 4.
Find the median for the data 8, 5, 7, 10, 15, 21.
Solution :
Arranging the given data in ascending order 5, 7, 8, 10, 15, 21
Hence, the median of the given data is 9.
Question 5.
Is the bar graph can be drawn using vertical bars?
Solution :
Yes, the bar graph can be drawn using vertical bars as well as horizontal bars.
Question 6.
The sum of 10 numbers is 550. Find their average number.
Solution :
Question 7.
What is the average of natural numbers from 1 to 67 ?
Solution :
Average of n natural numbers
= \(\frac{n+1}{2}\)
Here, n = 67
Average = \(\frac{67+1}{2}\) = \(\frac{68}{2}\) = 34
Connecting the Dots Class 7 Short Question Answer
Question 1.
Find the mean of the first ten even natural numbers.
Solution :
The first ten even natural numbers are 2,4,6,8,10,12,14,16,18, and 20. The mean is calculated by summing these numbers and dividing by the count, n = 10
Sum of observations = 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 = 30 + 30 + 30 + 20 = 110
Mean = \(\frac{110}{10}\) = 11
Therefore, the required mean is 11.
Question 2.
The mean of three numbers is 10. The mean of other four numbers is 12. Find the mean of all the numbers.
Solution :
Given, the mean of three numbers is 10.
The mean of the other four numbers is 12. We have to find the mean of all the numbers. We know, mean = sum of observations/number of observations
Sum of first 3 numbers = 10(3) = 30
Sum of other 4 numbers = 12(4) = 48
Sum of 7 numbers = 30 + 48 = 78
Number of observations = 7
Mean = 78 / 7=11.14
Therefore, the mean is 11.14.
Question 3.
Observe the given double bar graph and answer the questions given below.
a. How many girls like cricket?
b. Which is the most preferred sport of boys and girls?
c. Which sport is liked by 10 girls?
d. Which sport is liked by the same number of boys as that of the number of girls?
e. How many boys like football?
Solution :
a. No. of girls liking cricket are 5 in number.
b. For boys : Cricket
For girls : Basketball
c. Tennis
d. Tennis
e. 13 boys liked football.
Question 4.
The average age of 5 brothers born at intervals of 3 years is 14 years. Find the age of the eldest brother.
Solution :
Average age of 5 brothers = 14 years Total of ages = 14 × 5 = 70 years They are born at intervals of 3 years, so the ages can be written as :
x, x-3, x-6, x-9, x-12
Sum of the ages
x + (x-3) + (x-6) + (x-9)+ (x-12) = 70
5 x-30 = 70
5 x = 100
x = 20
Age of the eldest brother = 20 years
Question 5.
Is the mean of the first 30 natural numbers equal to the mean of the first 30 whole numbers? Justify your answer by calculating both the means.
Solution :
Mean of the first 30 natural numbers First 30 natural numbers: 1,2,3, ….., 30
Mean of the first 30 whole numbers First 30 whole numbers: 0,1,2, …., 29
Mean = Sum of first 30 whole numbers
= 14.5
No, the means are not equal. The difference arises because natural numbers start from 1 while whole numbers start from 0.
Question 6.
The median of the observations 8, 10, 12, 15, y+3,18,20,22,30 arranged in ascending order is 16. Find the value of y.
Solution :
Observations in ascending order : 8,10,12,15, y+3,18,20,22,30 Median : 16
Number of observations = 9 (odd)
Therefore, median is at the 5th position.
The 5th value = y + 3 = 16
y = 13
Connecting the Dots Class 7 Long Question Answer
Question 1.
Find the median of the given data if the mean is 4.5: 5,7,7,8, x, 5,4,3,1, 2
Solution :
Given, the data is 5,7,7,8, x, 5, 4, 3, 1, 2
Mean of the data is 4.5.
We have to find the median of the given data.
Sum of observations = 5+7+7+8+x+ 5+4+3+1+2=42+x
Number of observations = 10
Now,
4.5 = (42+x) / 10
42 + x = 4.5(10)
42 + x = 45
x = 45-42 = 3
Now, the data is 5,7,7,8,3,5,4,3,1,2
Arranging the data in ascending order, we get 1, 2, 3, 3, 4, 5, 5, 7, 7, 8
If n is even, then median
Therefore, the median is 4.5.