Question

Two employees are counting the number of broken eggs they find in the large 18 packs of eggs at the store they work at. The first employee records the following numbers of broken eggs in each pack:

0,0,1,1,1,1,1,2,2

(a) What is the median number of broken eggs in a pack?

(b) What is the mean number of broken eggs in a pack?
(c) What is the standard deviation of the number of broken eggs in a pack?

Suppose the second employee reports checking 35 more packs, and found every single pack had 1 broken egg. For the next questions, we will analyze the data of both employees combined (so the above numbers, together with 35 more entries of 1). You don’t need to compute the following statistics, but you need to compare them to the answers from parts a, b, and c with only the first employee’s numbers.

(d) How will the new information from the second employee change the mean? Why?

(e) How will the new information from the second employee change the standard deviation? Why?

Answer 1

a. The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

0   0   1   1   1   1   1   2   2   

So, the median is 1 .

b. Mean value is

c. Create the following table.

data	data-mean	(data - mean)2
0	-1	1
0	-1	1
1	0	0
1	0	0
1	0	0
1	0	0
1	0	0
2	1	1
2	1	1

Find the sum of numbers in the last column to get.

So standard deviation is

d. Here the value of each packs is 1, so the mean value will be also 1

e. As there is no variation among packs so there is 0 standard deviation for information from second employee