Question

Murder Rates The data represent the murder rate per 100,000 individuals in a sample of selected cities in the United States. Find the variance and standard deviation. Round your answers to at least one decimal place. Class limits Frequency 5-11 10 12-18 9 19-25 10 26-32 5 33-39 2 40-46 6

Answer 1

The Sample mean,Sample Variance, Standard deviation is mathematically given as

• x=21.66
• $\sigma=138.52$
• $\mu=11.769$

What is the Sample mean,Sample Variance, Standard deviation.?

Generally, the equation for Sample mean is  mathematically given as

$x = \frac{1}{N}(\sum xifi )$

Where

$\sum xifi=80+135+220+145+72+258$

$\sum xifi=910$

Therefore

x=1/42 (910)

x=21.66

Sample Variance

$\sigma = \frac{1}{N-1}(\sum xi^2fi-(\frac{1}{N}(\sum xifi^2 )) )$

Where

$\sum xi^2fi=640+2025+4840+4205+2592+11094$

$\sum xi^2fi=25396$

Therefore

$\sigma = \frac{1}{41}(25396-(\frac{1}{42}(910^2 )) )$

$\sigma=138.52$

Standard deviation.

$\mu=\sqrt{\sigma^2}\\\\\mu=\sqrt{138.52}$

$\mu=11.769$

In conclusion,

x=21.66

$\sigma=138.52$

$\mu=11.769$

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