Data and decision making

School of Economics and Finance
Faculty of Business
University of Tasmania
BEA 654 Data and Business Decision Making
Semester 2, 2013
CRICOS Provider Code 00586B
Partial Solutions to Problem Set 2—Week 3
1. Arithmetic mean= (-0.5+1)/2=0.25 (25%)
Geometric mean of annual rate of return RG
(1  RG ) 2  (1  (0.5))(1  1)
 R G  0 .5 * 2  1  0

The geometric mean reflects the true return of the investment.
2. c. See the formula.
3. The whole crew is present, so this is a population.
X = 567, X2 = 48,165, N=7
Ordered array of data: 49, 63, 77, 85, 94, 98, 101
Median position = (n+1)/2 = 4, median is 85
Mean = X/N = 567/7 = 81kg
2 = (X– (X)/N) 2 /N = 319.7142857,
 = 17.88.
Range = max-min = 101-49 = 52
4.
Calories Fat
240
260
350
350
420
510
530

8
3.5
22
20
16
22
19

Descriptive stats for calories:
Calories

Mean
380
Standard Error
42.7618
Median
350
Mode
350
Standard Deviation 113.1371
Sample Variance
12800
Kurtosis
-1.4478
Skewness
0.178848
Range
290
Minimum
240
Maximum
530
Sum
2660
Count
7
First quartile position: (n+1)/4 = 2. First quartile is 260. It means that 25% of ice coffees in the sample that have calories lower or equal to 260 and 75% of ice coffees that have calories higher or equal to 260.
Third quartile position: 3(n+1)/4 = 6. Third quartile is 510. It means that 75% of ice coffees in the sample that have calories lower or equal to 510 and 25% of ice coffees that have calories higher or equal to 510.

You need to know how to calculate standard deviation from a relatively small data set.
CV = 113.1371/380 = 29.77%. It means that the standard deviation of calories is about 30% of the size of the mean of calories.
Interquartile range is 250, which implies that 50% of middle-ranked calories are in this interquartile range.
Mean>Median, therefore slightly right skewed.
Descriptive stats for fat:
Fat
Mean
15.78571
Standard Error
2.746984
Median
19
Mode
22