Question

Math

Posted 6 months ago

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Tara is considering choosing either anthropology or economics as her college major, and she's wondering how her SAT scores compare to those of her peers in either major. Tara finds some data on the SAT scores of anthropology and economics majors at her school. The data is shown in the 2 plots below.
For $\square$ majors, the mean SAT score is greater than the median.
The $\square$ majors have a greater median SAT score.
Anthropology
Economics
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Answer from Sia

Posted 6 months ago

Solution by Steps

step 1

To determine which major has a mean SAT score greater than the median, we look at the shape of the distribution

step 2

A right-skewed distribution typically has a mean that is greater than the median

step 3

The Anthropology major's distribution is right-skewed, indicating that the mean is greater than the median for Anthropology

step 4

To determine which major has a greater median SAT score, we compare the center values of the distributions

step 5

The Economics major's distribution is more symmetrical, suggesting that the median is near the center of the distribution

step 6

Since the Economics distribution is centered higher on the SAT score scale than the Anthropology distribution, Economics has a greater median SAT score

[question 1] Answer

For Anthropology majors, the mean SAT score is greater than the median.
The Economics majors have a greater median SAT score.

Key Concept

Distribution Shape and Central Tendencies

Explanation

The shape of a distribution can indicate the relationship between the mean and median. A right-skewed distribution typically has a mean greater than the median, while a symmetrical distribution suggests the mean and median are close. The median is the middle value, so for a symmetrical distribution centered higher on the scale, the median will be higher.

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