Reference · module 8
Data and graphs
Everything this module explains, on one page.
Averages
Find the mean, the median and the range, and know which one to trust.
- The mean is what people usually call the average: add all the values and divide by how many there are. For 4, 8 and 9 the mean is 21 ÷ 3, which is 7.
- The median is the middle value once the numbers are sorted. For 3, 9, 4, 20, 5, sort to 3, 4, 5, 9, 20: the median is 5. With an even count, take the mean of the two middle values.
- One extreme value pulls the mean but barely moves the median, which is why salaries and house prices are often given as medians. The range, largest minus smallest, shows the spread.
The mistake you are about to make
median of 3, 9, 4, 20, 5 = 4
median of 3, 9, 4, 20, 5 = 5
The middle of the list as written looks like the median. The median is the middle of the sorted list: 3, 4, 5, 9, 20.
Coordinates
Place and read points on a grid, and measure between them.
- A point on a grid is given by two numbers in brackets: (x, y). The first says how far to go right, the second how far to go up, both counted from the origin (0, 0).
- Negative numbers go the other way: (−3, 2) is 3 left and 2 up. The order matters, so (2, 5) and (5, 2) are different points.
- Two points on the same horizontal line are as far apart as their x values differ: from (1, 4) to (7, 4) is 6 units. On a vertical line, compare the y values instead.
The mistake you are about to make
(2, 5) = 5 right, 2 up
(2, 5) = 2 right, 5 up
Up and down feels like the main direction on a page, so it seems to come first. x always comes first: along the corridor, then up the stairs.
Straight-line rules
Work with rules like y = 2x + 3 and read the slope and the starting value.
- A rule like y = 2x + 1 turns each x into a y. For x = 3, y is 2 × 3 + 1, which is 7. Plotting several such points gives a straight line.
- In y = 2x + 1 the 2 is the slope: every step to the right, the line climbs 2. The 1 is where it crosses the vertical axis, the value of y when x is 0.
- Taxi fares work this way: 3 euros to start plus 2 per km is y = 2x + 3. The starting fee is the crossing point, and the price per km is the slope.
The mistake you are about to make
x = 3 → 2x = 23
x = 3 → 2x = 6
2x is written with nothing between the 2 and the x, so with x = 3 it reads like the number 23. 2x means 2 times x: 6.