1) Put all the numbers in numerical order : 15, 23, 24, 25, 25, 25, 27 The median is the middle of the numbers : 25 Mode is the value that occurs more often : 25
2) Put all the numbers in numerical order : 2, 3, 3, 3, 3, 4, 4, 5 The middle of the numbers is 3 and 3 so, 3 + 3 = 6 6 : 2 = 3
Median = 3 Mode = 3
3) Put all the numbers in numerical order : 5, 7, 8, 9, 9, 10, 10, 10, 12 Median = 9 Mode = 10
4) Put all the numbers in numerical order : 0, 1, 1, 2, 2, 3, 3, 3, 4, 4
Median 2 + 3 = 5 : 2 = 2,5 Mode = 3
5) Put all the numbers in numerical order : 12, 13, 15, 18, 25 Median = 15 Mode = 0 (None)
6) Put all the numbers in numerical order : 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5 Median = 3 Mode = 3 and 4
7) Put all the numbers in numerical order : 6, 8, 9, 10, 10, 12
Median 9 + 10 = 19 : 2 = 8 Mode = 10
8) Put all the numbers in numerical order : 28, 30, 30, 30, 30, 31, 31, 31, 31, 31, 31, 31
Thanks to the Pythagorean Theorem we know that with any right triangle, A^2+B^2=C^2. In this case we can use 15^2+15^2=sqrt of 450. The square root of 450 is 15 times the square root of 2. Thus x=15√2. Now we need to find y. All angles in a triangle add up to 180 so if we have 45+45+y=180 then y=90.
Two events are independent of each other, this is called Compound Probability. Classical example is if two coins are filped, what is the probability of getting two heads in a row.?
Answer: each has 50% probability because there are two states only, either H or T. since we have two coins the probability of getting two heads in row is the product of obtaining heads for each individual coin (which is independent of each other). or is × = = 25%. (Notice!).
Back to our problem, now here we have 3 paint brands and one of them is the right paint brand and two of them are not correct brands. so the prabablity that the customer has picked not correct brand is and her husband has not picked correct brand is also , since two probabilities are compound probabilities i.e indepandant of each other the probablity that both woman and her husband fail get correct brand is the product of the two and is = × = .