Question

1. Find the sample mean and sample standard deviation of your data.
2. What is the Z score?
3. Pick three bills from the last 12 months and change the values into z-scores. What does the z-score tell you about that particular month?
4. Between what two values would be considered a normal bill? Remember, being within 2 Standard Deviations is considered normal.
5. Are any of your bills in the last 12 months unusual? Very unusual?
6. Are there times when you would accept an "unusual" bill? Explain.

Data

	Data
1	223
2	200
3	154
4	217
5	223
6	157
7	178
8	159
9	747
10	243
11	325
12	298

Answer 1

From the data above the mean of the 12-month data is calculated as

$\bar{x}=\frac{x1+x2+...+xn}{n}=\frac{223+200+...+298}{12}=260.333$

and standard deviation as

N 1 N 1 s2= (X-)2 N 1 (223 - 260.33333333333)2 + (298 - 260.33333333333)2 12-1 + 290082.66666667 11 -26371.151515152 26371.151515152 162.391968752

s=160.392

since within 2 standard deviations it is considered as usual value hence

value at -2 standard deviations is

260.333-2*160.391

=-60.451

and also value at +2 standard deviation as

260.333+2*160.391

=581.117

hence all values except 9th month that is 747 appear abnormal