Answer:
a) shoe size 12
b) shoe size 11
c) 10.85 or 217/20
Explanation:
a) The mode refers to the number which appears the most often in the data. Be careful not to just think it is the number you see the most in the frequency part of the table. Here the answer would be shoe size 12, as the frequency is 8, which means 8 people have that shoe size. This is the biggest amount of people who have the same shoe size.
To visualise this, you could think about it with all the number in a line:
9, 9, 10, 10, 10, 10,..... 12, 12, 12, 12, 12, 12.....
Since there would be eight 12s in the list (which is the biggest number of any shoe size in the data), 12 would be the mode.
b) The median is the middle value of the data. So all you need to do is count the number of values that there are. So here it would be the number of players. To do this, you need to count up the frequencies of all the different shoe sizes. 2 + 7 + 3 + 8 = 20 Then divide by 2 to find the middle of the frequency. 20/2 = 10 Therefore you're looking for the 10th value in the table. So it can't be shoe size 9 or shoe size 10, as adding their frequencies together only adds up to 9. This means that the median has to be in the next shoe size, which in this case is shoe size 11.
c) To find the mean, you need to add up all the shoe sizes and divide it by the number of players there are. So (9*2) + (10*7) + (11*3) + (12*8) = 217 (There are 2 players with shoe size 9, so you need to add each shoe size the number of times that their frequency indicates, which is why I multiplied them.) There are 20 players in the table. I know this by adding up all the frequencies. 217/20 = 10.85