Maths · Rung 27 of 30

Spread

The mean says where the centre is; the spread says how far the values stray from it. The range is the distance from the largest to the smallest, and the standard deviation is how far values sit from the mean on average. Two series with the same mean can be one flat and the other wild.

Where this sits

This is where the ladder starts: nothing is needed before it.

Exercises from this rung

Generated by the app, from easiest to hardest

  1. In the series 5, 6, 7, 8, 30, which measure does not change if 30 became 255?

    • The median
    • The mean
    • The standard deviation
    • The range

    Why The median is the middle value, 7, and it stays put however much the largest grows. The mean, the range and the standard deviation rise with it.

    easier

  2. In the series 3, 4, 5, 6, 28, which measure does not change if 28 became 253?

    • The median
    • The standard deviation
    • The mean
    • The range

    Why The median is the middle value, 5, and it stays put however much the largest grows. The mean, the range and the standard deviation rise with it.

    in between

  3. What is the standard deviation?

    • 9
    • 4
    • 2
    • 12

    Why The mean is 9. The distances are 0, 2, 2, 4, 4, 6 and 6; their squares add up to 112, divided by 7 gives 16, and the square root is 4.

    harder