Q 3.27 - 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

Medieval Cremation Burials. In the article "Material Cul ture as Memory: Combs and Cremations in Early Medieval Britain (Early Medieval Europe, Vol. 12. Issue 2. pp. 89-128), H. Williams discussed the frequency of cremation burials found in 17 archaeological sites in eastem England. Here are the data. 

$$\begin{gathered} 83 64 46 523 35 34 265 2484 \\ 46 385 21 86 429 51 258 119 \end{gathered}$$

Step-by-Step Solution

Answer

$$\begin{gathered} a) 292.8 \\ b) 83 \\ c) 46 \end{gathered}$$

Step 1. Given information.

We have given data :$83 64 46 523 35 34 265 2484 46 385 21 86 429 51 258 119$

Step 2. Mean of the data.

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

$$\begin{gathered} =\frac{83+64+46+523+35+34+265 2484+46+385+21+86+429+51+258 +119}{17} \\ = 292.7647059 \\ =292.8 \end{gathered}$$

Step 3. Median of the data.

Arrange the data in increasing order : $21,34, 35, 46, 46, 48, 51, 64 \left(83\right) , 86 ,119, 258, 265, 385, 523, 2480$

The number of observation is $17$

The median is the  middle observation in the ordered list.

Median $=83$

Step 4. Mode of the data.

The greatest frequency is the mode of the data set. 

The mode of the given data set is $46$