Question
A football manager needs to pick his team for the next match. He gets some information on players in the team from previous matches. He needs to choose between two players based on their work rate. He measures their work rate using average and variation of the distance they covered. & multicolumn(7)(|c|)( Distance covered for previous matches (km) ) Player A & 7.2 & 6.8 & 7.6 & 8.7 & 7.4 & 6.8 & 8.0 Player B & 7.9 & 7.3 & 5.8 & 7.6 & DNP & DNP & 6.9 "DNP = Did Not Play Which player should the manager choose? Make two comments with reference to average distance and variation in distances.
Answer
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Seren
Professional · Tutor for 6 years
Answer
Upon comparing both values and considering the manager needs for distance coverage and consistency in that, a player with more average distance and less Absolute mean deviation should be selected. [The final answer is obtained AFTER executing the calculations.]
Explanation
## Step1:Firstly, calculate the average distance covered by Player A and Player B. The number of previous matches for Player A is 7 and for Player B is 5.Then,###
Let's apply the formula:For Player A:
For Player B:
## Step2:Next, calculate the Absolute mean deviation as a measure of distance covered as a measure of consistency. Less absolute mean deviation means more consistency.###
This formula represents the tougher calculated concept.-
= Absolute value of the difference of xi(current value) from the mean value(
).-
= Number of observations.Then SUM the differences. Then divide it with
.Applies the formula again:For Player A: \(Absolute\;mean\;deviation = \frac{((7.2-7.5)+(6.8-7.5)+(7.6-7.5)+(8.7-7.5)+(7.4-7.5)+(6.8-7.5)+(8.0-7.5))}{7}\)For Player B: \(Absolute\;mean\;deviation = \frac{((7.9-7.1)+(7.3-7.1)+(5.8-7.1)+(7.6-7.1)+(6.9-7.1))}{5}\)Please note that we are using the average distance calculated in Step1 for the mean distance in this equation.