1. ## Business Statistics: Tchebysheff's Theorem

This is a three part question and I'm stuck on the third part, if someone could please help.

Consider the following set of sample data:
78 121 143 88 110 107 62 122 130 95 78 139 89 125

a. Compute the mean and the standard deviation for these sample data.

b. Calculate the coefficient of variation for these sample data and interpret its meaning.

I don't know what it means by interpret it's meaning....

c. Using Tchebysheff's Theorem, determine the range of values that should include at least 89% of the data. Count the number of data values that fall into this range and comment on whether your interval range was conservative or not.

2. Originally Posted by lisa1984wilson
This is a three part question and I'm stuck on the third part, if someone could please help.

Consider the following set of sample data:
78 121 143 88 110 107 62 122 130 95 78 139 89 125

a. Compute the mean and the standard deviation for these sample data.

b. Calculate the coefficient of variation for these sample data and interpret its meaning.

I don't know what it means by interpret it's meaning....

c. Using Tchebysheff's Theorem, determine the range of values that should include at least 89% of the data. Count the number of data values that fall into this range and comment on whether your interval range was conservative or not.
You require the value of $\displaystyle \alpha$ such that $\displaystyle \Pr(|X - \mu| \leq \alpha) \geq 0.89 \Rightarrow \Pr(|X - \mu| \geq \alpha)\leq 0.11$ .

Tchebysheff's Theorem (one of the equivalent forms): $\displaystyle \Pr(|X - \mu| \geq \alpha) \leq \frac{\sigma^2}{\alpha^2}$.

So you require the value of $\displaystyle \alpha$ such that $\displaystyle \frac{\sigma^2}{\alpha^2} = 0.11$.