Q 3.22. - Elementary Statistics

Question

Find the 

a. Mean    b. median    c. mode

For the mean and the median, round each answer to one more decimal place than that used for the observations.

Technical Merit. In one Winter Olympics, Michelle Kwan competed in the Short Program ladies singles event. From nine judges, she received scores ranging from I (poor) to 6 (perfect). The following table provides the scores that the judges gave her on technical merit, found in an article by S. Berry .

$5.8 5.7 5.9 5.7 5.5 5.7 5.7 5.7 5.6$

Step-by-Step Solution

Answer

$$\begin{gathered} a) 5.7 \\ b) 5.7 \\ c) 5.7 \end{gathered}$$

Step 1. Given information.

We have given data: $5.8 5.7 5.9 5.7 5.5 5.7 5.7 5.7 5.6$

Step 2. Mean of the data.

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

$$\begin{gathered} =\frac{5.8+ 5.7+5.9+5.7+5.5+5.7+5.7+5.7+5.6}{9} \\ =\frac{51.3}{9} \\ =5.7 \end{gathered}$$

Step 3. Median of the data.

Arrange the data in increasing order : 

$5.5 5.6 5.7 5.7 (5.7) 5.7 5.7 5.8 5.9$

The number of observation is  $9$

The median is the  middle observation in the ordered list.

Median$=5.7$

Step 4. Mode of the data.

The greatest frequency is the mode of the data set. 

The mode of the given data set is $5.7$.