Question

42. Jacquez is a scientist running a month-long experiment on the growth of E. Coliin warm and cool environments. He put cultures into 10 different petri dishes foreach environment. Below are the population sizes of each petri dish at the end ofthe experiment.

Answer 1

- Visualizing the plots of both populations, we have:

Question 1:

- The above plot is for the Warm population. It is a histogram with bin size of 20

- The modal bin is the 80 - 100 bin. The mean is going to lower than the mode and median of the distribution because the distribution is skewed to the left because of the 0-20 bin.

- For the Cool distribution, we have:

- The distribution is not well formed because there are few samples.

- The mean, median, and mode of the distribution are within the 40-60 bin.

- At the moment, the distribution has a right-skew.

Question 2:

`\begin{gathered} \text{ Warm:} \\ \text{ Mean:} \\ (61+100+13+96+68+89+80+74+96+56)/(10)=(733)/(10)=73.3 \\ \\ \text{ Median:} \\ \text{ The median is simply the average of the middle numbers of the distribution.} \\ \text{ let us rearrange the dataset in ascending order} \\ 61,100,13,96,68,89,80,74,96,56 \\ 13,56,61,68,74,80,89,96,96,100 \\ \text{ The two middle numbers are 74 and 80} \\ \text{ Thus, Median becomes:} \\ (74+80)/(2)=77 \\ \\ \\ \text{ Mode:} \\ \text{ This is simply the value that occurs the most.} \\ \text{ Mode }=96 \end{gathered}`

`\begin{gathered} \text{ Cool:} \\ \text{ Mean}=(53+7+73+4+70+82+73+40+50+10)/(10)=(462)/(10)=46.2 \\ \\ \text{ Median:} \\ 53,7,73,4,70,82,73,40,50,10 \\ \text{ Rearrange:} \\ 4,7,10,40,50,53,70,73,73,82 \\ Median=(50+53)/(2)=51.5 \\ \\ \\ \text{ Mode:} \\ 73\text{ is the mode since it occurs the most} \end{gathered}`