Recently we did a practice GCSE statistics paper at school, and here is the question everyone got wrong:
Freddie has 10 innings during the cricket season.
His scores were as follows:
0, 12, 65, 74, 34, 125, 98, 4, 6, 36
Q1: What was his median score?
Q2: What was the range of his scores?
Q3: Which type of average is best suited to the data? Median (Middle No.), Mode (No. that appears most) or Mean (sum of data divided by how many pieces of data)
Q1 and 2 are straightfoward, nearly everyone got them right.
But almost everyone got Q3 wrong, as the answer was median and not mean.
This means that according to the marker, the best way to work out a batting average is to line up all the scores low to high and pick the middle number, not the mean which is a normal cricket average.
Two points: I wrote mean as soon as I had read the question, as it is common knowledge a batting average is runs/times out. The only people who got it right had no knowledge of cricket averages at all. Surely the majority of the world (the cricket community) is right?
And in the possibility of a median average being the correct answer, why do we use the mean instead of the median. (Form, year by year analysis, accuracy, fluctuating numbers)
Smiths 'median average' is 50. In his next four innings he scores: 300, 200, 35 and 40, yet as the 50 will still be the middle number, his 'median' does not change.