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Nov 2018 p62 q5
2423
The Quivers Archery club has 12 Junior members and 20 Senior members. For the Junior members, the mean age is 15.5 years and the standard deviation of the ages is 1.2 years. The ages of the Senior members are summarised by \(\Sigma y = 910\) and \(\Sigma y^2 = 42\,850\), where \(y\) is the age of a Senior member in years.
(i) Find the mean age of all 32 members of the club.
(ii) Find the standard deviation of the ages of all 32 members of the club.
Solution
(i) To find the mean age of all 32 members, calculate the total age of all members and divide by the total number of members:
\(\text{Total age of Juniors} = 15.5 \times 12 = 186\)
\(\text{Total age of Seniors} = 910\)
\(\text{Total age of all members} = 186 + 910 = 1096\)