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? 85 69 42 49 535 32 31 284 2085 42 362 24 86 415 51 244 110 a. the mean is. (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? 85 69 42 49 535 32 31 284 2085 42 362 24 86 415 51 244 110 a. the mean is. (round to one decimal place as needed.)

Answer

Explanation:

Step1: Calculate sum of data

Sum = (85 + 69+42 + 49+535+32+31+284+2085+42+362+24+86+415+51+244+110) [ \begin{align*} &85 + 69+42 + 49+535+32+31+284+2085+42+362+24+86+415+51+244+110\ =&(85+69)+(42 + 49)+535+(32+31)+284+2085+(42+362)+24+86+415+51+244+110\ =&154+91+535+63+284+2085+404+24+86+415+51+244+110\ =&(154 + 91)+535+63+284+2085+404+24+86+415+51+244+110\ =&245+535+63+284+2085+404+24+86+415+51+244+110\ =&(245+535)+63+284+2085+404+24+86+415+51+244+110\ =&780+63+284+2085+404+24+86+415+51+244+110\ =&(780+63)+284+2085+404+24+86+415+51+244+110\ =&843+284+2085+404+24+86+415+51+244+110\ =&(843+284)+2085+404+24+86+415+51+244+110\ =&1127+2085+404+24+86+415+51+244+110\ =&(1127+2085)+404+24+86+415+51+244+110\ =&3212+404+24+86+415+51+244+110\ =&(3212+404)+24+86+415+51+244+110\ =&3616+24+86+415+51+244+110\ =&(3616+24)+86+415+51+244+110\ =&3640+86+415+51+244+110\ =&(3640+86)+415+51+244+110\ =&3726+415+51+244+110\ =&(3726+415)+51+244+110\ =&4141+51+244+110\ =&(4141+51)+244+110\ =&4192+244+110\ =&(4192+244)+110\ =&4436+110\ =&4546 \end{align*} ]

Step2: Calculate the mean

The number of data points (n = 17). Mean (\bar{x}=\frac{\text{Sum}}{n}=\frac{4546}{17}\approx267.4)

Step3: Arrange data in ascending - order

(24,31,32,42,42,49,51,69,85,86,110,244,284,362,415,535,2085)

Step4: Calculate the median

Since (n = 17) (odd), the median is the (\left(\frac{n + 1}{2}\right))-th value. (\frac{17+1}{2}=9) - th value. So the median is (85).

Step5: Calculate the mode

The mode is the value that appears most frequently. Here, (42) appears twice and other values appear only once, so the mode is (42).

Step6: Discuss the best - measure of center

The data has extreme values (such as (2085) and (535)). The mean is affected by these extreme values. The median is a better measure of center as it is not influenced by extreme values and gives a more representative value of the "center" of the data set.

Answer:

a. The mean is (267.4), the median is (85), the mode is (42). b. The median works best here.