Question

the data below are the frequency of cremation burials found in 17 archaeological sites. a. obtain the mean, median, and mode of these data. b. which measure of center do you think works best here? 85 63 45 48 513 33 32 289 2391 45 358 28 85 416 60 237 125 a. the mean is (round to one decimal place as needed.)

Explanation:

Step1: Sum all the data values

First, we list out all the data points: 85, 63, 45, 48, 513, 33, 32, 289, 2391, 45, 358, 28, 85, 416, 60, 237, 125.
Now we sum them up:
\[

$$\begin{align*} &85 + 63 + 45 + 48 + 513 + 33 + 32 + 289 + 2391 + 45 + 358 + 28 + 85 + 416 + 60 + 237 + 125\\ =& (85 + 63) + (45 + 48) + 513 + 33 + 32 + 289 + 2391 + (45 + 358) + 28 + (85 + 416) + 60 + 237 + 125\\ =& 148 + 93 + 513 + 33 + 32 + 289 + 2391 + 403 + 28 + 501 + 60 + 237 + 125\\ =& (148 + 93) + 513 + 33 + 32 + 289 + 2391 + 403 + 28 + 501 + 60 + 237 + 125\\ =& 241 + 513 + 33 + 32 + 289 + 2391 + 403 + 28 + 501 + 60 + 237 + 125\\ =& (241 + 513) + 33 + 32 + 289 + 2391 + 403 + 28 + 501 + 60 + 237 + 125\\ =& 754 + 33 + 32 + 289 + 2391 + 403 + 28 + 501 + 60 + 237 + 125\\ =& (754 + 33) + 32 + 289 + 2391 + 403 + 28 + 501 + 60 + 237 + 125\\ =& 787 + 32 + 289 + 2391 + 403 + 28 + 501 + 60 + 237 + 125\\ =& (787 + 32) + 289 + 2391 + 403 + 28 + 501 + 60 + 237 + 125\\ =& 819 + 289 + 2391 + 403 + 28 + 501 + 60 + 237 + 125\\ =& (819 + 289) + 2391 + 403 + 28 + 501 + 60 + 237 + 125\\ =& 1108 + 2391 + 403 + 28 + 501 + 60 + 237 + 125\\ =& (1108 + 2391) + 403 + 28 + 501 + 60 + 237 + 125\\ =& 3499 + 403 + 28 + 501 + 60 + 237 + 125\\ =& (3499 + 403) + 28 + 501 + 60 + 237 + 125\\ =& 3902 + 28 + 501 + 60 + 237 + 125\\ =& (3902 + 28) + 501 + 60 + 237 + 125\\ =& 3930 + 501 + 60 + 237 + 125\\ =& (3930 + 501) + 60 + 237 + 125\\ =& 4431 + 60 + 237 + 125\\ =& (4431 + 60) + 237 + 125\\ =& 4491 + 237 + 125\\ =& (4491 + 237) + 125\\ =& 4728 + 125\\ =& 4853 \end{align*}$$

\]

Step2: Calculate the mean

The mean is the sum of the data divided by the number of data points. There are 17 data points. So the mean \( \bar{x} = \frac{\text{Sum of data}}{\text{Number of data points}}=\frac{4853}{17}\approx285.5 \) (rounded to one decimal place).

Answer:

285.5