NCERT Solutions Ganita Prakash (Part 2) Chapter 5 In-text Questions — The Balancing Act

Book page 103 Updated on2026-09-05

Q1.

Consider any 2 numbers. Find their average/arithmetic mean. Repeat this by taking other pairs. What do you observe?

Answer

For two numbers the mean always lands exactly halfway between them.

3 and 7 → (3 + 7) ÷ 2 = 5, and 5 is 2 away from each
8 and 9 → (8 + 9) ÷ 2 = 8.5, and 8.5 is 0.5 away from each
40 and 100 → (40 + 100) ÷ 2 = 70, and 70 is 30 away from each

Why it happens: take any two numbers p and q with p < q. Their mean is (p + q) ÷ 2. Its distance from p is (p + q)/2 − p = (q − p)/2, and its distance from q is q − (p + q)/2 = (q − p)/2. The two distances are the same expression, so the mean must sit at the midpoint.

Tip: this is the first hint of the big idea of this section — the mean is the point that balances the data. With two numbers, balancing simply means standing midway.

Q2.

Calculate and mark the mean of each collection of data below.

Answer

Reading the four dot plots on page 103 and computing each mean:

Dot plot	Values	Sum	Mean
Top left (blue)	6, 7, 8	21	21 ÷ 3 = 7
Top right (blue)	3, 6, 9	18	18 ÷ 3 = 6
Bottom left (yellow)	2, 4, 9	15	15 ÷ 3 = 5
Bottom right (yellow)	4, 11, 15	30	30 ÷ 3 = 10

Mark each mean with a small cross on the number line of that plot: at 7, 6, 5 and 10.

Check it yourself: in the first plot the mean 7 is also the middle dot, but in the third plot the mean 5 is not one of the dots at all, and it is not the midpoint of 2 and 9 either. So ‘centre’ here must mean something other than ‘middle dot’ — that is exactly what page 104 sorts out.

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