the data below are the frequency of cremation burials found in 17 archaeological sites. a. obtain the mean…

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? 84 60 46 49 522 34 33 285 2377 46 377 29 88 410 56 236 110 a. the mean is 270.7. (round to one decimal place as needed.)

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? 84 60 46 49 522 34 33 285 2377 46 377 29 88 410 56 236 110 a. the mean is 270.7. (round to one decimal place as needed.)

Answer

Explanation:

Step1: Calculate the sum of data

Sum all the values: $84 + 60+46+49+522+34+33+285+2377+46+377+29+88+410+56+236+110 = 4601$

Step2: Calculate the mean

The mean $\bar{x}=\frac{\text{Sum of data}}{\text{Number of data points}}$. There are $n = 17$ data - points. So, $\bar{x}=\frac{4601}{17}\approx270.7$

Step3: Find the median

Arrange the data in ascending order: $29,33,34,46,46,49,56,60,84,88,110,236,285,377,410,522,2377$. Since $n = 17$ (an odd number), the median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{17+1}{2}=9$-th value, which is $84$.

Step4: Find the mode

The mode is the value that appears most frequently. The number $46$ appears twice, and all other numbers appear only once, so the mode is $46$.

Step5: Discuss the best measure of center

The data set has a large outlier ($2377$). The mean is affected by outliers. The median is a better measure of the center as it is not influenced by extreme values. The mode is not a very representative measure here as it only represents the most frequently - occurring value which may not be indicative of the overall data distribution.

Answer:

a. Mean: $270.7$, Median: $84$, Mode: $46$ b. The median works best here.