Question

1. the geometry test scores for andrea and joe are shown in the table below

andrea\tjoe
82\t91
87\t78
90\t94
84\t67
which statement about their test scores is correct?
(1) both the mean and standard deviation of andrea’s test scores are higher than joe’s.
(2) both the mean and standard deviation of joe’s test scores are higher than andrea’s.
(3) the mean of andrea’s test scores is higher than joe’s, but joe’s standard deviation is higher than andrea’s.
(4) the mean of joe’s test scores is higher than andrea’s, but andrea’s standard deviation is higher than joe’s.
hint:
1.
2.
3.

Explanation:

Step1: Calculate Andrea's mean

Andrea's scores: 82, 87, 90, 84.
Mean formula: $\bar{x} = \frac{\sum x}{n}$
$\sum x = 82 + 87 + 90 + 84 = 343$
$n = 4$
$\bar{x}_{Andrea} = \frac{343}{4} = 85.75$

Step2: Calculate Joe's mean

Joe's scores: 91, 78, 94, 67.
$\sum x = 91 + 78 + 94 + 67 = 330$
$\bar{x}_{Joe} = \frac{330}{4} = 82.5$

Step3: Analyze standard deviation (conceptually)

Andrea's scores: 82, 87, 90, 84. These are close to each other (range: 90 - 82 = 8).
Joe's scores: 91, 78, 94, 67. These are more spread out (range: 94 - 67 = 27). So Joe's standard deviation is higher.

Step4: Evaluate options

• (1): Andrea’s mean (85.75) > Joe’s (82.5), but Joe’s SD is higher. Eliminate.
• (2): Joe’s mean (82.5) < Andrea’s (85.75). Eliminate.
• (3): Andrea’s mean (85.75) > Joe’s (82.5), Joe’s SD (more spread) > Andrea’s. Correct.
• (4): Joe’s mean (82.5) < Andrea’s (85.75). Eliminate.

Answer:

(3) The mean of Andrea’s test scores is higher than Joe’s, but Joe’s standard deviation is higher than Andrea’s.