Question

Descriptive Statistics:

In certain states, savings banks are permitted to sell life insurance. The approval process consists of underwriting, which includes a review of the application, a medical information bureau check, possible requests for additional medical information and medical exams, and a policy compilation stage, in which the policy pages are generated and sent to the bank for delivery. The ability to deliver approved policies to customers in a timely manner is critical to the profitability of this service to the bank. Let’s define the variable of interest as the total processing time in days. You collect the data by selecting a random sample of 27 approved policies during a period of one month:

73, 19, 16, 64, 28, 28, 31, 90, 60, 56, 31, 56, 22, 18, 45, 48, 17, 17, 17, 91, 92, 63, 50, 51, 69, 16, 17

1. Compute the mean, median and mode

2. Compute the range, interquartile range, variance, standard deviation ** for IQR would it be 61.5-18.5=43 OR 63-18=45??

3. Construct a frequency table and a histogram. Are the data skewed? If so, how?

4. What would you tell a customer who enters the bank to purchase this type of insurance policy and asks how long the approval process takes?

Answer 1

Mean	43.88889
Standard Error	4.865816
Median	45
Mode	17
Standard Deviation	25.28352
Sample Variance	639.2564
Kurtosis	-0.90407
Skewness	0.517268
Range	76
Minimum	16
Maximum	92
Sum	1185
Count	27

Q3=63 Q1=18

IQR=Q3-Q1=45

Bin	Frequency
10	0
20	8
30	3
40	2
50	3
60	4
70	3
80	1
90	1
100	2
More	0

Data is positively skewed. (as data is right tailed and skewness=0.5>0)