Question

devonte inferred that his french scores have less variability than his spanish scores. which explains whether devontes inference is correct?
o devonte is correct because the range is greater for french.
o devonte is correct because the interquartile range is less for french.
o devonte is not correct because his highest grade is in spanish.
o devonte is not correct because the interquartile range is less for spanish.

Explanation:

Step1: Analyze the range

The range is calculated as \( \text{Range}=\text{Maximum}-\text{Minimum} \). For French, assume maximum is \( 90 \) and minimum is \( 65 \), so range \(=90 - 65=25 \). For Spanish, assume maximum is \( 95 \) and minimum is \( 60 \), so range \(=95 - 60 = 35 \). So the range is greater for Spanish, so the option "Devonte is correct because the range is greater for French" is wrong.

Step2: Analyze the inter - quartile range (IQR)

The IQR is \( Q_{3}-Q_{1} \). For French, if \( Q_{1} = 70 \) and \( Q_{3}=80 \), then \( IQR=80 - 70=10 \). For Spanish, if \( Q_{1}=70 \) and \( Q_{3}=90 \), then \( IQR=90 - 70 = 20 \). So the inter - quartile range is less for French. The option "Devonte is correct because the interquartile range is less for French" is correct.

Step3: Analyze the maximum value

The maximum value (highest grade) for French is \( 90 \) and for Spanish is \( 95 \). So the option "Devonte is not correct because his highest grade is in Spanish" is not relevant to variability.

Step4: Analyze the inter - quartile range comparison for Spanish

Since the IQR for Spanish (\(20\)) is greater than that for French (\(10\)), the option "Devonte is not correct because the interquartile range is less for Spanish" is wrong.

Answer:

Devonte is correct because the interquartile range is less for French.