Two crates each contain 750 objects. The double box-and-whisker plot shows the median weights of 50 random samples of 10 objects from each crate. Can you determine which crate weighs more? Explain.

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Solution

Step 1: Calculate the data for crate A
Data of crate $A = 6 6.5 7.5 9 9.5$
Median of crate $A = 7.5$
Mean of crate A = $A = 6 + 6.5 + 7.5 + 9 + 9.5 \div 5 = 38.5 \div 5 = 7.7$
IQR = $9 - 6.5 = 2.5$
Step 2: Calculate the data for crate B
Data of crate $B = 9 10 11 12.5 13.5$
Median of crate $B = 11$
IQR = $12.5 - 10 = 2.5$
Mean of crate B = $B = (9 + 10 + 11 + 12.5 + 13.5) \div 5 = 56 \div 5 = 11.2$
The variation in the center of crate B is greater than the measure of crate A. The variation of crate A is similar to the variation of crate B.
Hence, Crate B weighs more than Crate A.

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Q. A crate contains

750

fruits. The weight of

10

fruits from the crate taken at random are shown in the given table. Can we determine if this sample of

10

fruits can represent the whole crate in terms of weight?
MAD of the crate

= 0.5

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