Question

latesha and bernard are playing a game. their scores for five games are shown in the table below.
lateshas and bernards scores
lateshas scores 92 45 67 36 80
bernards scores 63 68 62 69 53
which statement comparing the means to the ranges is true?
the means differ by 1, but the ranges differ by 40.
the means differ by 1, but the ranges differ by 2.
the means differ by 5, but the ranges differ by 40.
the means differ by 5, but the ranges differ by 2.

Explanation:

Step1: Calculate LaTesha's mean

$\text{Mean}_{\text{LaTesha}} = \frac{92 + 45 + 67 + 36 + 80}{5} = \frac{320}{5} = 64$

Step2: Calculate Bernard's mean

$\text{Mean}_{\text{Bernard}} = \frac{63 + 68 + 62 + 69 + 53}{5} = \frac{315}{5} = 63$

Step3: Find difference of means

$64 - 63 = 1$

Step4: Calculate LaTesha's range

$\text{Range}_{\text{LaTesha}} = 92 - 36 = 56$

Step5: Calculate Bernard's range

$\text{Range}_{\text{Bernard}} = 69 - 53 = 16$

Step6: Find difference of ranges

$56 - 16 = 40$

Answer:

The means differ by 1, but the ranges differ by 40.