Solution to Homework 6

Problem 1::
Mean: ∑X = 457, so =457/26 = 17.6
Median: the ordered dataset is
1 3 4 4 5 7 7 9 9 9 10 10 11 12 13 17 19 25 26 27 27 32 34 37 42 57

the two observations in the middle are 11 and 12, so median=(11+12)/2 = 11.5
Using MINITAB: Stat > Basic Statistics > Display Descriptive Statistics, Variable= cases

b) Neither is very interesting. The main point of this dataset is how the number of cases changes over time, so the best thing to do is draw the scatterplot of cases by year:

Problem 2
The incomes of the employees with a job level of 7 are
28400 39100 28600 87400 78400 56800 45100 54300 78600 51700 71000 41000 40400 11000 78600 96300 61500 72200
(use Data>Subset Worksheet> Rows that match Condition: 'Job Level' = 7)
so
∑ X = 1,020,400
= 1020400/18 = 56689
∑ X2 = 66,920,140,000
so
Sxx = ∑X2-(∑X)2/n = 66920140000-10204002/18 = 9,074,797,778
and
s = √Sxx/(n-1) = 23104.4

MINITAB: Stat > Basic Statistics > Display Descriptive Statistics, Variable=Income , By variables=Job Level