Q 3.21 - 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.

Tornado Touchdowns: Each year, tomadoes that touchdown are recorded by the Storm Prediction Center and published in Monthly Tom Statistics. The following table gives the number of tomados that touched down in the United States during each month of one year.

$$\begin{gathered} 3 2 47 118 204 97 \\ 68 86 62 57 98 99 \end{gathered}$$

Step-by-Step Solution

Answer

$$\begin{gathered} a)78.4 \\ b) 77.0 \end{gathered}$$

$c)$ No mode exist.

Step 1. Given information.

We have given data: $$\begin{gathered} 3 2 47 118 204 97 \\ 68 86 62 57 98 99 \end{gathered}$$

Step 2. Mean of the data.

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

$$\begin{gathered} =\frac{3+2+47+118+204+97+68+86+62+57+98+99}{12} \\ =\frac{941}{12} \\ =78.4 \end{gathered}$$

Step 3. Median of the data.

Arrange the data in increasing order : $2 3 47 57 62 \left(68\right) \left(86\right) 97 98 99 118 204$

The number of observation is $12$.

The median is the mean of the  two  middle observation in the ordered list.

Median

$$\begin{gathered} =\frac{68+86}{2} \\ =\frac{154}{2} \\ =77.0 \end{gathered}$$

Step 4. Mode of the data.

The greatest frequency is the mode of the data set. 

There is no mode exist for the data set.