Download Descriptive Statistics

Descriptive Statistics
1. Grades on Business Statistics Exam
The relative frequency is how often something happens divided by all outcomes. All
relative frequencies add up to 1. The frequency of getting an A was 16 and the relative
frequency of getting an A is 8%. All this means is that 16 people out of the 200 would
receive an A 8% of the time, which was the smallest. The largest frequency was 90
people receiving an A 45% of the time.
2. The Journal of Consumer Marketing
12 consumers out of 286 would receive a letter; refund check, and a coupon 4% of the
time. 76 consumers out of the 286 would receive a letter only 26% of the time.
3. A Sample of 20 Measurements
There are 20 measurements. The stem is the first digit and the leaf is the last digit. For
example 26 would be split into 2 (stem) and 6 (leaf). The stem values are listed down
and the leaf values are listed next to them. This way the stem groups the measurements
and each leaf indicates a measurement within that group.
4. A Sample of 20 Measurements
1 class out of 20 would be in the class interval of 10.5 – 15.5 5%. 5 classes out of 20
would be in the class interval of 25.5 – 30.5 25%.
5. The sigma sign means to sum things up.
A. Sum of all the values in the set.
B. Sum of each value in the set squared.
C. Sum of all the values in the set minus 5 and then square.
D. Sum of all the values in the set minus 2 and then square.
E. Sum of all the values in the set squared.
6. The mean is adding up all the numbers and then divide by how many numbers there were
(7+3+4+1+5+6)/6. The median is the middle number of all the values or the mean of the
two middle numbers (4+5)/2= 4.5.
7. The range is the difference between the lowest and the highest value in a set (9-0=9).
The variance is the sum of each data point squared minus the mean divided by the
number of data points (155-4.6/4)=37.6. The standard deviation is the square root of the
variance. Each value in the data set minus the mean squared divided by the total number
of data points minus one (3-4.6)^2 + (9-4.6) ^2 + (0-4.6) ^2 + (7-4.6) ^2 + (4-4.6)^ 2 /(51) = 2.56+19.36+21.16+5.76+. 36/4 = 49.2/4 = 12.3 = 3.50.
8. Z score is the difference between the value and the mean divided by the standard
deviation (8.8-11/2=-1.1 and 0-(-5)/1.5=3.333). The larger the Z score, the greater the
distance from the value to the mean. From these two examples, I can see that 0 lies the
greater distance above the mean and 8.8 lies the greatest distance below the mean.
9. A. The mean is adding up all 25 beta numbers and then divide by 25 ( 26.813)/25 =
1.073). The variance is the sum of each data point squared minus the mean divided by
25, which equals 0.225313. Standard deviation is the square root of the variance, which
equal 0.474671. All 25 values lie within the ranges. This result does agree with the
Empirical rule because all 25 values lie within the range, and they are symmetric and
highly skewed.
B. There are 25 numbers in ascending order. 0.987 is the middle number in 1 – 25. This
means that 12 numbers are less than 0.987 and 12 are greater than 0.987. There are 12
beta values that changed faster than the average market price and 12 numbers that
changed slower than market price.
C. The 80th percentile of the 25 beta values is the 21st number, which is 1.502. Percentile
is equal to 80 x (25+1)/100 = 20.8 or 21.
D. Z score is the difference between the value of Sears and Roebuck stock and the mean
divided by the standard deviation (0.688-1.073)/0.144671 = -0.81008.