Please show calculations so that I may learn how to do this on my own. PLEASE NO

Question

Please show calculations so that I may learn how to do this on my own. PLEASE NO EXCEL! Thank you!

2. The time of individual student on Midterm Exam was: 1. Time Spent: 2:15 2. Time Spent: 1:24 3. Time Spent: 2:46 4. Time Spent: 1:58 5. Time Spent: 2:00 6. Time Spent:2:28 7. Time Spent: 2:36 8. Time Spent: 1:24 9. Time Spent: 2:28 10.Time Spent: 2:25 11. Time Spent: 1:47 12. Time Spent: 2:15 Show detail of your work a) What is the Mode(s)?) Answer: b) What is Median? Answer: c) what is the Variance of Sample Answer:- d) What is the standard Deviation of Population Answer:

Explanation / Answer

Solution:
Time spent on midterm exam is as follows:
2.15, 1.24, 2.46, 1.58, 2, 2.28, 2.36, 1.24, 2.28, 2.25, 1.47, 2.15

After sorting the data we found
1.24, 1.24, 1.47, 1.58, 2, 2.15, 2.15, 2.25, 2.28, 2.28, 2.36, 2.46

Solution(a):
Mode of the time spent on individual student is
there are three modes of the individual student time spend
1.24, 2.15, 2.28

Solution(b):
Median of the time spent on individual student is
(12+1)/2 or 6.5th value
So median of the time spent is = (2.15+2.15)/2 = 4.30/2 = 2.15

Solution(c):
Mean of the time spent = 23.46/12 = 1.955
Variance of the time spent = ((1.24-1.955)^2 +(1.24-1.955)^2 +(1.47-1.955)^2 +(1.58-1.955)^2 +(2-1.955)^2 +(2.15-1.955)^2 +(2.15-1.955)^2 + (2.25-1.955)^2 +(2.28-1.955)^2 + (2.28-1.955)^2 + (2.36-1.955)^2 +(2.46-1.955)^2 )/11
Variance = (0.511225 + 0.511225 + 0.23525 + 0.140625 + 0.002025 + 0.038025 + 0.038025 + 0.087025 + 0.105625 + 0.105625 + 0.164025 + 0.255025)/11 = 2.193725/11 = 0.199429

so sample variance = 0.199429
Solution(4)
Sample standard deviation = sqrt(variance) = sqrt(0.199429) = 0.427562

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