Q 3.5. - Elementary Statistics

Question

Consider the data set: $1,2,3,4,5,6,7,8,9$.

a) Obtain the mean and median of the data.

b) Replace the $9$ in the data set by $99$ and again compare the mean and median. Decide which measure of the center works better here and explain your answer.

c) For the data set in part b) the mean is neither central nor typical for the data. The lack of what property of the mean accounts for this result.

Step-by-Step Solution

Answer

a) Mean $=5$ and median $=5$

b) Mean $=15$ and median$=5$

c) The mean is neither central nor typical for the data. Since lack of resistance property of the mean accounts 

Step 1. Given information.

Consider the data set:  $1,2,3,4,5,6,7,8,9$.

Step 2. Obtain the mean and median of the data.

Mean=$\frac{Sum of all observation}{Number of observation}$

$$\begin{gathered} =\frac{1+12+3+4+5+6+7+8+9}{9} \\ =\frac{45}{9} \\ =5 \end{gathered}$$

Median is the middle of the observation.

So, median $=5$

Step 3. Replace the 9 in the data set by 99 and again compare the mean and median. Decide which measure of the center works better here and explain your answer.

Mean=$$\begin{gathered} \frac{1+2+3+4+5+6+7+8+99}{9} \\ =\frac{135}{9} \\ =15 \end{gathered}$$

Median is the middle of the observation.

Median $=5$

Step 4. For the data set in part b) the mean is neither central nor typical for the data. The lack of what property of the mean accounts for this result.

The mean is neither central nor typical for the data. Since lack of resistance property of the mean accounts