The Kellen school district gives awards to its schools based on overall student attendance. The data for attendance are shown in the table, where Low represents the fewest days attended and High represents the most days attended for a single student.

School Low High Range Mean Median IRQ σ
High School W 108 180 72 169 150 47.5 29.5
High School X 112 180 68 160 124 49.5 32.4
High School Z 130 180 50 162 151 39.5 27.5

Part A: If the school district wants to award the school that has the most consistent attendance among its students, which high school should it choose and why? Justif

Question

The Kellen school district gives awards to its schools based on overall student attendance. The data for attendance are shown in the table, where Low represents the fewest days attended and High represents the most days attended for a single student.


School	Low	High	Range	Mean	Median	IRQ	σ
High School W	108	180	72	169	150	47.5	29.5
High School X	112	180	68	160	124	49.5	32.4
High School Z	130	180	50	162	151	39.5	27.5


Part A: If the school district wants to award the school that has the most consistent attendance among its students, which high school should it choose and why? Justif

help_people · Answer

Part A: If the school district wants to award the school that has the most consistent attendance among its students, which high school should it choose and why? Justify your answer mathematically. (5 points)

Part B: If the school district wants to award the school with the highest average attendance, which school should it choose and why? Justify your answer mathematically. (5 points)

michele_laino · Answer

please wait, I'm pondering...

help_people · Answer

ok

michele_laino · Answer

I'm not sure, nevertheless I think school Z, since a lower \sigma, means a more narrow distribution, furthermore school X and school Y have a lower "Low" values than school Z

michele_laino · Answer

please wait, I ask for help to another helper

michele_laino · Answer

@Loser66  please help

loser66 · Answer

I am not got at statistics/probability. I am sorry.

michele_laino · Answer

@ganeshie8  please help

michele_laino · Answer

@freckles  please help

michele_laino · Answer

@mathmate  please help

michele_laino · Answer

@oleg3321  please help

michele_laino · Answer

for part B I think that the answer is school X, since school X has the highest mean

michele_laino · Answer

oops.. school W not school X

loser66 · Answer

To me, for a) I choose Z since the $\sigma $ is smallest. That means the consistent is highest. One more reason, for L = 130 , and H = 180, we can see that the fewest day the student attendance is higher than other while the highest day is the same with others. 
for b) I choose W  (the reason is its mean is highest, like what you choose)

loser66 · Answer

But, don't rely on me. I am not good at statistics.

michele_laino · Answer

yes! I also used the value of \sigma, since the value of \sigma tells us the shape of the distribution

loser66 · Answer

hehehe...me too.

help_people · Answer

ok thanks you guys :) i would date to ask but could dyou help w. one more