
difference from mean 
difference squared 
1  6 = 5 
25 
3  6 = 3 
9 
7  6 = 1 
1 
9  6 = 3 
9 
10  6 = 4 
16 
sum = 0 
sum = 60 
The variance is 60/4 = 12; the standard deviation is the square root of 12 or approximately 3.464.
2. Mike has started running, hoping to run a marathon in six months. For the last six days, his running times (in minutes) have been: 39, 43, 68, 40, 49, 61.
Mean: 300/6 = 50
No mode
Median = 46, midpoint between 43 and 49, the two middle
times
Range: 6839 = 29 minutes
difference from
mean difference
squared 39  50 =
11 121 43  50 =
7 49 68  50 =
18 324 40  50 =
10 100 49  50 =
1 1 61  50 =
11 121 sum =
0 sum =
716
The variance is 716/5= 143.2; the standard deviation is the square root of 143.2 or approximately 11.96.
3. Gretchen has caught six lake trout. These are their
weights:
20 oz, 24 oz, 30oz, 28 oz, 18 oz, 18 oz.
Mean = 23, median = 22; mode
12
Range = 12; st. dev. = 5.178
4. Joan has collected data on gasoline prices from six area stations: $1.09 $1.11 $1.27 $1.13 $1.15 $1.15
Mean = $1.15; median = $1.14; mode = $1.15.
Range = $.18; the standard deviation is the square root of
.0040 or about $.0632.
5. You have a sample of eight items. You have computed the mean, and the following are seven of the deviations from the mean: 1, 2, 4, 7, 3, 1, 2. What is the variance of this sample?
The series must sum to zero, so the missing number is 4. Squaring and summing gives 100, dividing by seven gives 14.29
6. If the standard deviation of a group of numbers is zero, what can you conclude?
All the numbers must be the same.
7. The table below gives the percentile ranks of the cumulative grade point averages for the junior class as the end of the 197576 school year.
Percentile: GPA 90 3.72 80 3.53 75 3.40 50 3.01 25 2.54 20 2.44 10 2.14
The interdecile range is the
difference of thee 10th percentile from the 90th percentile,
or 3.72  2.14 = 1.58
The median is the middle or the 50th percentile,
3.01
8. Suppose the students at Apex College have a mean SAT verbal plus math score of 950 with a standard deviation of 250. At nearby Apogee University the students have an average SAT total of 1000 with a standard deviation of 100. How would you explain the differences in the student bodies of these two schools to someone who did not know what the mean and standard deviation were?
At Apogee the kids are pretty bright, and though there are clear differences between the top and bottom of the student body, those differences are not nearly as noticeable as the difference at Apex. The top students at Apex are brighter than the top students at Apogee, but there are a whole lot more students at Apex who struggle with anything that is too academic.