3 years ago

The average basketball has a diameter of 9.5 inches. What is the volume of an average basketball?

Mathematics

1 answer:

Elodia [21]3 years ago

6 0

the formula for volume of sphere is 4/3||r^3

diameter=2radius

in the formula we need to have radius but we have been given diameter so we convert diameter to radius

d=2r

r=d/2

9.5÷2

4.75

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<h3>How to determine standard deviation?</h3>

The table of values is given as:

x f(x)

0-3 13

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8-11 10

12-15 11

16-19 0

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Rewrite the table by calculating the class midpoints:

x f(x)

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Start by calculating the mean using:

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This gives

$\bar x = \frac{1.5 * 13 + 5.5 * 13 + 9.5 * 10 + 13.5 * 11 + 17.5 * 0 + 21.5 * 3}{13 + 13 + 10 + 11 + 0 +3}$

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The standard deviation is then calculated as:

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

So, we have:

$\sigma= \sqrt{\frac{13 * (1.5 - 7.98)^2 + 13 * (5.5 - 7.98)^2 + (9.5 - 7.98)^2 * 10 + (13.5 - 7.98)^2 * 11 + (17.5 - 7.98)^2 * 0 + (21.5 - 7.98)^2 * 3}{13 + 13 + 10 + 11 + 0 +3}}$

Evaluate

$\sigma= \sqrt{30.6496}$

Solve

$\sigma= 5.54$

Hence, the standard deviation is 5.54

Read more about standard deviation at:

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