# Hard Statisitics question

• January 17th 2009, 11:52 AM
nerdo
Hard Statisitics question
Hi can some help me with this question as i don't understand it at all, and just do not know were to begin. (Headbang)
• January 17th 2009, 03:09 PM
Last_Singularity
Quote:

Originally Posted by nerdo
Hi can some help me with this question as i don't understand it at all, and just do not know were to begin. (Headbang)

Attachment 9695

I can get you started.

Part A:
There are a lot choices. Simply pick a measurement in units of customary and metric. Example: pounds vs. kilograms, miles vs. kilometers, Fahrenheit vs. Celsius, etc.

For instance, take a temperature conversion. We know that the relationship between F and C is: $F = 9/5 C + 32$.

So if $y_i$ represented Fahrenheit and $x_i$ represented Celsius, then $a$ is $9/5$ and $b$ is 32.

Part B:
(i)
$\bar{y} = \frac{1}{n} \sum_{i=1}^{n} y_i = \frac{1}{n} \sum_{i=1}^{n} (a x_i + b) = \frac{a}{n} \sum_{i=1}^{n} x_i + \frac{1}{n} \sum_{i=1}^{n} b = a \bar{x_i} + b$

So the claim is true, as proven by algebra above.

(ii)
For $\bar{z}$, the claim is false. It is up to you to find a counterexample. Pick any arbitrary set of values for $x_i$ and see whether or not $\bar{z} = \frac{1}{n} \sum_{i=1}^{n} \frac{c}{x_i}$ is equal to $\frac{c}{\bar{x}}$. Most likely not, if you picked your values strategically.

(iii)
Since the relationship between $y_i,x_i$ is linear (and thus bijective), the ordering of the values of $x_i$ are preserved during a mapping to $y_i$. Thus, the smallest value of $x_i$ gets sent to the smallest value of $y_i$. Same with the largest value and the median, etc.

(iv)
Again, find a counterexample.