A farmer keeps sheep in two separate fields on his land and weighs each flock before the autumn sale. Field A has 8 sheep with a mean mass of 62 kg. Field B...
Question 1 Report
A farmer keeps sheep in two separate fields on his land and weighs each flock before the autumn sale. Field A has 8 sheep with a mean mass of 62 kg. Field B has 12 sheep with a mean mass of 58 kg.
- Work out the mean mass of all 20 sheep in the two fields combined. (3)
Answer Details
Combining two flocks means adding their total masses together before dividing by the combined number of sheep, not averaging the two field means directly, since the fields hold different numbers of sheep.
Total mass in Field A = \(8\times62=496\) kg. [1 mark] Total mass in Field B = \(12\times58=696\) kg. [1 mark] Combined mean = \((496+696)\div20=1192\div20=59.6\) kg. [1 mark]
This combined mean sits closer to Field B's mean of \(58\) kg than to Field A's mean of \(62\) kg, because Field B contributes more sheep to the total.
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