Description
1- Roll a single die 50 times and record the results. Now use that data set to compute the mean, median, mode, variance, and standard deviation of the set.
2- Consider a standard deck of cards (52 with each of four suits – club, diamond, heart, spade) and drawing two cards. What is the probability of two hearts with replacement? Without replacement?
Explanation & Answer
The solutions are ready. Please read them and ask if something is unclear. I can explain further if you want.docx and pdf files are identical
1. Roll a single die 50 times and record the results. Now use that data set to compute the mean,
median, mode, variance, and standard deviation of the set.
The results of rolling: 1, 3, 2, 2, 5, 4, 4, 2, 5, 5, 2, 1, 4, 6, 6, 2, 2, 3, 1, 1, 2, 2, 4, 6, 6, 2, 3, 1, 1, 1, 2, 3,
1, 5, 4, 4, 3, 6, 6, 1, 1, 1, 3, 4, 1, 1, 6, 3, 6, 4.
There are 13 1’s, 10 2’s, 7 3’s, 8 4’s, 4 5’s, 8 6’s.
The mean is the arithmetic mean, the sum divided by the number of rolls (50). The sum is
13 ∙ 1 + 10 ∙ 2 + 7 ∙ 3 + 8 ∙ 4 + 4 ∙ 5 + 8 ∙ 6 = 13 + 20 + 21 + 32 + 20 + 48 =
= 34 + 40 + 80 = 154,
154
308
so the mean is 50 = 100 = 𝟑. 𝟎𝟖.
The median is the center number in sorted list (average between two most centered numbers for an
even quantity of numbers). Here the sorted list is
11111111111112222222222333333344444444555566666666.
Remove 12 items from the left and from the right: 12222222222333333344444444.
Then remove 8 more items: 2223333333.
Now we see that both center numbers are 3’s, so the median is 3.
The mode is the number whic...