NCERT Solutions for Class 8th Maths Chapter 5 Tales by Dots and Lines
Updated on 2026-09-19
About this chapter
The mean is the balance point of the data: the distances of the values below it add up to exactly the same total as the distances of the values above it. That is why there is only one mean. Adding a value bigger than the mean pulls the mean up; a smaller one pulls it down; a value equal to the mean changes nothing. Two values can be added on opposite sides so that the mean does not move at all. If every value goes up by k, the mean goes up by k. If every value is multiplied by k, the mean is multiplied by k. Both facts are proved with algebra in the chapter. The median is the middle value of the sorted data. Because it only counts positions, one stray extreme value barely moves it, while the same value can swing the mean a lot. With a frequency table, the mean is (sum of value × frequency)
- The Balancing Act
- Unchanging Mean!
- Relatively Unchanged!
- Tinkering with Median
- Finding the Unknown
- Mean and Median with Frequencies
- Spreadsheets
- Visualising and Interpreting Data
- Space Jam: A Traffic Problem in the Future?
- Catch the (Pattern in) Rain
Quick revision
| Idea | What it means | Worked example | Why it matters |
|---|---|---|---|
| Mean | Sum of values ÷ number of values | 3, 5, 10, 12 → 30 ÷ 4 = 7.5 | Uses every value, so every value can move it |
| Mean as balance point | Total distance on the left = total distance on the right | For 3, 5, 10, 12 about 7.5: 4.5 + 2.5 = 2.5 + 4.5 | Explains why there is exactly one mean |
| Adding a value | Above the mean → mean rises; below → mean falls; equal → no change | New mean − old mean = (x − a) ÷ (n + 1) | Predict the shift without recomputing |
| Shifting all values | Add k to every value → mean increases by k | Mean of 8, 3, 10, ... is 7.18; add 10 → 17.18 | Turns a long sum into one addition |
| Scaling all values | Multiply every value by k → mean is multiplied by k | 7.18 × 2 = 14.36 | Change of units needs no fresh calculation |
| Median | Middle value of the sorted data | 4, 7, 8, 12, 14 → median 8 | Ignores how far away the extremes are |
| Median with an even count | Average of the two middle values | 4, 7, 8, 11, 12, 14 → (8 + 11) ÷ 2 = 9.5 | Keeps the middle honest when n is even |
| Mean from a frequency table | Σ(value × frequency) ÷ Σ(frequency) | 188 ÷ 36 = 5.22 family members | Repeated values must be counted every time |
| Median from a frequency table | Add frequencies until you pass the middle position | 18th and 19th of 36 values are both 5 | No need to write out all the values |
| Line graph | Points joined in time order; steepness shows the rate of change | Objects launched into space, 2012–2024 | Shows a trend that 52 bars would hide |
| Reading a graph | Step 1: identify what is given. Step 2: infer only what is supported | “In 2023 there were no power cuts” is not supported | Guards against reading in what is not there |
| Infographic / strip | A picture where colour or shade carries the number | 48 half-hour boxes = one full day | A whole day, or a whole country, at a glance |
Exercises
- In-text Questions — The Balancing Act Page 103
- In-text Questions — The Balancing Act Page 104
- In-text Questions — The Balancing Act Page 105
- Unchanging Mean! — In-text Questions Page 105–106
- Relatively Unchanged! — In-text Questions Page 106–107
- Relatively Unchanged! — In-text Questions Page 107
- Tinkering with Median — In-text Questions Page 108
- Finding the Unknown — In-text Questions Page 109
- Mean and Median with Frequencies — In-text Questions Page 110
- Spreadsheets — In-text Questions Page 112–113
- Figure it Out — The Balancing Act Page 113–116
- In-text Questions — Visualising and Interpreting Data Page 116–119
- Space Jam: A Traffic Problem in the Future? — In-text Questions Page 119–120
- Catch the (Pattern in) Rain — In-text Questions Page 120–121
- Figure it Out — Visualising and Interpreting Data Page 122–123
- Infographics — In-text Questions Page 123–124
- What can a Strip Say? — In-text Questions Page 125
- What can a Strip Say? — In-text Questions Page 126
- Data Story: Sleepy-Deepy — In-text Questions Page 126–127
- Figure it Out — Visualising and Interpreting Data Page 127–132