Question

1. Consider two universities, A and B. Suppose we survey 10 alumni from each university and ask them how many years it took to complete their degree. University A is more prestigious and students tend to graduate sooner. Their responses were {3,3, 3, 4,4,4, 4, 4, 5,5}. On the other hand University B is more relaxed. Their 10 alumni answered in the following 3, 4, 4,4,5, 5, 5,5,5, 6}. Make a hist ogram of each of the data sets. How do you expect the mean, variance, and skewness would compare between the two classes? Compute the mean, variance of each class and compare them to see if your suspicions were correct. Make a guess about whether the skewness would be positive or negative for each data set

Answer 1

Sr.NO. A (B-Bbar)^2 2.56 2 3 4 5 6 : (A-Abar)^2 0.81 0.81 0.81 0.01 0.01 0.01 0.01 0.01 1.21 | 1.21 4.9 uuuuu AAA w 0.36 0.36 0.36 0.16 0.16 0.16 0.16 0.16 1.96 6.4 8 4. 10 5 39 6 46 Total

from the above table, n = 10 A fos university A:- ZA = 39 ° Mean of A=TA - 38 - 3.9 Varance (A) (A-A) - 4.9 0.5444 n-1 SD(A) = vranance ca) = V0.5444 = 0.7378 mode (A) = 4( maximum repeted value) Skewness (A): Mean - mode SD = 3.9 - 4 0.7378 Skewness (A) = -0.1355 ® for University 'B' - IB E46 meam 05 BPIB-46 - 0.6 Variance (B) = I (B-B)2 = 6.4 0.711 D- 19 SDC B)- Vraniance (B) = 10.7111 = 0.8432 repeated value) mode (B) = 5 : Maximum skewness (B) = Mean - Mode SD 4.6-5 0.8432 skewnen(B) = -0.4743

Histogram for University A Histogram of University B 1 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10

xplanation from Comparing mean of university A and B we can say that, university of B requise mose years to complete their degree t we are comparsing variances of university A and B, we can say Vannonce (3) 7 Variance (A) you - O. TILL 7 0.5464 Hence uni. B have more variation for complete their degree and last t we compare skewness of both wrivent ties both we can say from Histogram of uni. I and Histogram of university B are both | Negatively skewed. Hence skewness would be negative for each data. set