Answer: (a) The chart is in the first attachment named table frequency.
(b) The histogram is in the second attachment named frequency vs. enrollment
(c) Mode
(d) x = 9071.4
(e) s = 6677.64
(f) It is -0.16 standard deviation away
Step-by-step explanation:
(c) Mode is the number in the data set which appears more often. When thinking about builiding a new community college, if you choose mode will have which college enrollment will appear more often, i.e., which courses have more students wanting to enroll.
(d) To calculate sample mean of a frequency data:
1) Find the midpoint for each interval;
2) Multiply each midpoint for its correspondent frequency;
3) Sum up each multiplication obtained in the previous step;
4) Sum up all the frequencies;
5) Divide the sum in step 3 by the sum in step 4;
For this chart:
x = [tex]\frac{3000.10+7500.16+12500.3+17500.3+22500.1+27500.2}{35}[/tex]
x = 9071.4
(e) To find the standard deviation:
1) With each midpoint, calculate its square;
2) Multiply the midppoint square by its correspondent frequency;
3) Use the following formula to determine the sample standard:
s = √∑f.M² - n(μ)² / n-1
For this chart:
s = [tex]\sqrt{\frac{4396250000 - 35*(9071.4)^{2}}{34} }[/tex]
s = 6677.64
(f) To find how many standard deviations away is the enrollment:
z = [tex]\frac{8000-9071.4}{6677.64}[/tex]
z = - 0.16
8000 enrollments are -0.16 standard deviations away from the mean.
