Mean, median, mode and spread: watch it solved step by step

Mean, median, mode, range, quartiles, variance and standard deviation of a data set, with the deviations table. Level: KS3 / A-level. Type any problem of this kind and the Lab works it out and animates every move, with a plain-words explanation of why.

Worked example: 12, 15, 11, 18, 15, 9, 20

The data. There are 7 values. Statistics starts by listing them, and sorting them from smallest to largest, because the median and quartiles need the order.
Put them in order. Smallest to largest. Nothing is removed: the same values, just in order.
The mean. The mean is the "fair share" value: add everything up, then divide by how many there are.
The median. With an odd number of values the median is the middle one: value number 4.
The mode. The mode is the value that appears most often: here 2 times.
Range and quartiles. The range is the spread from smallest to largest. The quartiles split the ordered data into four equal-sized groups: Q_1 is the median of the lower half, Q_3 the median of the upper half (the middle value is left out of both halves when n is odd).
How far is each value from the mean?. Subtract the mean from each value (the deviations always add to 0), then square each one so that negatives cannot cancel the positives.
Variance. The variance is the average squared deviation. Divide by n for a whole population, or by n-1 when the data is a sample of a bigger group.
Standard deviation. The standard deviation is the square root of the variance: it brings the spread back to the same units as the data.
Check. The mean must lie between the smallest and largest values, and the standard deviation can never be larger than the range.

Answer: mean = 100/7 (≈ 14.2857), median = 15, mode = 15, SD (population) ≈ 3.614

Practise mean, median, mode and spread with problems the Lab marks for you.