Question

Each crate contains 750 fruits. The weight of 10 fruits from each crate taken at random are as shown in the table.
Can you determine if this sample of 10 fruits can represent the whole crate in terms of weight?
MAD of the crate = 0.5

Number of fruits	Weight (in lb)
1	0.8
2	1
3	1.2
2	2
2	2.4

Answer 1

Mean of the given sample = x
$=\frac{\text{Total weight of the fruits}}{\text{Number of fruits}}=\frac{(0.8\times 1)+(1\times 2)+(1.2\times 3)+(2\times 2)+(2.4\times 2)}{1+2+3+2+2}=\frac{0.8+2+3.6+4+4.8}{10}=\frac{15.2}{10}=1.52$

MAD of the given sample $=\frac{\text{Sum of all deviations}}{\text{Total number of fruits taken}}=\frac{(|0.8-1.52|\times 1)+(|1-1.52|\times 2)+(|1.2-1.52|\times 3)+(|2-1.52|\times 2)+(|2.4-1.52|\times 2)}{1+2+3+2+2}$

$=\frac{0.72+1.04+0.96+0.96+1.76}{10}=\frac{5.44}{10}=0.544$

Since the MAD of the sample taken does not match with the MAD of the fruit crate, so this sample cannot represent the given crate of fruits.