Transition Year Maths Example 3:


An American professional basketball team publishes its players’ wages. They have one exceptional star player. The wages per annum are: $360,000, $380,000, $400,000, $420,000, $460,000, $490,000, $500,000, $500,000, $520,000, $530,000, $600,000, $5,640,000. Find the mean, mode, median and comment on the suitability of each average


Mean


= 350 00, 0 380 000 … 5 640 000 12


Median Mode $500,000 (only figure which occurs twice)


= =


$, $, $,= 495 000


490 000 500 000 2


+


In this example, for an ordinary player considering signing to play for the team, the median or the mode gives him a better idea of what he may earn. The mean is affected by the very high wages of one exceptional player. This is called outlier.


Normal Distribution Example 4:


remembered 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Frequency 2 0 2 3 7 5 8 10 15 13 11 9 5 4 2 2 0 0 1 1 0


Digits


Plot the data on a bar chart, the frequency goes on the y-axis. Find the three averages, for this data, the mean, the mode and the median.


Mean = total number of digits remembered total number of pupils


= 2 0 012 ×+× + × +×+ × × + ×


202 3 1 …


2337 4…1 19 0 20 +++ + + 0


= · 837


Mode = the most common number of numbers remembered = 8 Median = line all the numbers remembered in a row and the median is the middle one, or the average of the two middle ones if it is an even


number i.e. = + =88 2


8


++ + ==,, , ,


10 800 000 12


, $,000900 0


100 pupils were shown a 20 digit number for 30 seconds and then asked to recall the number. The number of digits they could remember and repeat before they made a mistake was recorded:


20


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