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lilavasa [31]
2 years ago
14

A sample of 25 undergraduates reported the following dollar amounts of entertainment expenses last year:

Mathematics
1 answer:
marin [14]2 years ago
4 0

Answer:

Range = 85

\sigma = 28.71

Interval = [666.78, 781.62]

Step-by-step explanation:

Given

The data for 25 undergraduates

Solving (a): Range and Standard deviation

The range is:

Range = Highest - Least

From the dataset:

Highest = 772

Least = 687

So:

Range = Highest - Least

Range = 772-687

Range = 85

The standard deviation is:

\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}

First, calculate the mean

\bar x = \frac{769 +691 +............+715}{25}

\bar x = \frac{18105}{25}

\bar x = 724.2

So, the standard deviation is:

\sigma = \sqrt{\frac{(769-724.2)^2 +(691-724.2)^2 +(699-724.2)^2 +(730-724.2)^2 +............+(715-724.2)^2}{25}}

\sigma = \sqrt{\frac{20604}{25}}

\sigma = \sqrt{824.16}

\sigma = 28.71

Solving (b): The interval of the 95% of the observation.

Using the emperical rule, we have:

Interval = [\bar x - 2*\sigma, \bar x+ 2*\sigma]

Interval = [724.2 - 2*28.71, 724.2 + 2*28.71]

Interval = [666.78, 781.62]

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