a) The median number of goals scored is 3.
b) The mean number of goals scored is 2.33.
In the question, we are given a table showing the number of goals a football team conceded in a season.
a) We are asked to find the median number of goals scored.
The median for any frequency distribution is the middle value of the cumulative frequency distribution.
The cumulative frequency distribution for the given table can be shown as follows:
Conceded Goals _ Frequency _ Cumulative Frequency
_____0_______ ______2_____ ________2_________
_____1_______ ______8_____ _______10_________
_____2_______ ______4_____ _______14_________
_____3_______ _____10_____ _______24_________
_____4_______ ______6_____ _______30_________
The total number of observations is 30.
The middlemost frequency is the average of the 15th and 16th observations, that is, 3.
Thus, the median number of goals scored is 3.
b) We are asked to find the mean number of goals conceded per match.
The mean is given by the formula, μ = {∑xf}/{∑f}, where μ is the mean, x is the variable, and f is the frequency of the variable.
Thus, the mean number of goals conceded = { (0*2) + (1*8) + (2*4) + (3*10) + (4*6) }/{ 2 + 8 + 4 + 10 + 6} = { 0 + 8 + 8 + 30 + 24 }/{30} = 70/30 = 2.33.
Thus, the mean number of goals scored is 2.33.
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