Solution
- 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:
[tex]\begin{gathered} \text{ Warm:} \\ \text{ Mean:} \\ \frac{61+100+13+96+68+89+80+74+96+56}{10}=\frac{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:} \\ \frac{74+80}{2}=77 \\ \\ \\ \text{ Mode:} \\ \text{ This is simply the value that occurs the most.} \\ \text{ Mode }=96 \end{gathered}[/tex][tex]\begin{gathered} \text{ Cool:} \\ \text{ Mean}=\frac{53+7+73+4+70+82+73+40+50+10}{10}=\frac{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=\frac{50+53}{2}=51.5 \\ \\ \\ \text{ Mode:} \\ 73\text{ is the mode since it occurs the most} \end{gathered}[/tex]
