Fill in the blanks such that the median of the collection is 13 : 5, 21, 14, How many possibilities exist Class 8

Fill in the blanks such that the median of the collection is 13 : 5, 21, 14, How many possibilities exist Class 8

Question 1.

Fill in the blanks such that the median of the collection is 13 : 5, 21, 14, ______, ______, _____. How many possibilities exist if only counting numbers are allowed? Class 8

Solution:

5, 21, 14, 7, 12, 25.

Infinitely many possibilities.

Question 2.

Fill in the blanks such that the mean of the collection is 6.5 : 3, 11, _____, ______, 15, 6. How many possibilities exist if only counting numbers are allowed? Class 8

Solution:

3, 11, 1, 3, 15, 6 or 3, 11, 2, 2, 15, 6.

Two possibilities.

Question 3.

Check whether each of the statements below is true. Justify your reasoning. Use algebra, if necessary, to justify. Class 8

(i) The average of two even numbers is even.

(ii) The average of any two multiples of 5 will be a multiple of 5.

(iii) The average of any 5 multiples of 5 will also be a multiple of 5.

Solution:

(i) Not true. For example, average of 6 and 8 is 7.

(ii) Not true. For example, average of 5 and 10 is 7.5.

(iii) Not true. For example, average of 5, 10, 15, 20 and 30 is [latex]\frac{80}{5}[/latex] = 16, which is not a multiple of 5.