Question

a grocery store buys oranges from two different farmers. the mean weight of farmer as oranges is 8 oz. the mean weight of farmer bs oranges is 9.1 oz. the mad of both data sets is 2. what can you infer about the two sets of oranges?

• the mad is large.
• the data sets are very different.
• the variabilities of the sets of oranges are similar.
• the mean is small.

Explanation:

Compare the Mean Absolute Deviation (MAD) of both data sets

$$ \text{MAD of Farmer A's oranges} = 2 $$

$$ \text{MAD of Farmer B's oranges} = 2 $$

Relate MAD to variability

$$ \text{MAD} = \text{Measure of variability} $$

$$ \text{Equal MAD values} \implies \text{Similar variabilities} $$

Evaluate the given options

$$ \text{Option 3 matches the conclusion: "The variabilities of the sets of oranges are similar."} $$

Answer:

• The MAD is large.
• The data sets are very different.
• The variabilities of the sets of oranges are similar. (Correct answer)
• The mean is small.