Statistics, Year 7: more practice

5.5

HintPut the numbers in order first, and notice how many there are.

The whyIn order: 3, 4, 4, 7, 9, 12. There are six values, so the median is halfway between the 3rd and 4th: (4 + 7) ÷ 2 = 5.5.

As a diagonal line across the first four

HintThink of how tallies are grouped so they are quick to count.

The whyThe first four tallies are upright strokes and the fifth crosses them, so each group stands for 5 and can be counted in fives.

So the height of each bar alone shows its frequency

HintThink about what the reader is comparing.

The whyIf widths differed, the bigger area of a wide bar could look more important. With equal widths, only the heights change, so the comparison is fair.

21

HintHalf a symbol is half of the key's value.

The why3 × 6 = 18 and half a symbol is 3, so 18 + 3 = 21. Equivalently, 3.5 × 6 = 21.

3½ symbols

HintDivide the number of cars by the number each symbol stands for.

The why14 ÷ 4 = 3.5, so three whole symbols and one half symbol show 14 cars.

21:15

HintAdd the hours first, then deal with the minutes crossing the hour.

The why18:50 plus 2 hours is 20:50, and plus 25 minutes is 21:15, because 50 + 25 = 75 minutes is 1 hour 15 minutes.

The temperature stayed the same

HintThe line goes along but not up or down.

The whyA flat line means no change in the value while time went on, so the temperature was constant over that spell.

3

HintFirst find the total rise, then the time it took.

The whyThe rise is 20 − 14 = 6 °C over 2 hours, so 6 ÷ 2 = 3 °C per hour.

Presenting (organising) the data

HintThink about what you do before you can interpret anything.

The whyThe cycle runs: pose a question, collect data, present it in tables or charts, then interpret and conclude. Presenting makes the pattern visible.

8

HintTurn the mean back into a total before adding the new number.

The whyThe first total is 6 × 7 = 42. Adding 14 gives 56, and 56 ÷ 7 = 8.