Stats
Tutorial Questions for Exploratory Data Analysis – Summary Statistics & Graphs
1. Customers of a particular bank rated the service provided by the bank on a scale of one to ten, correct to one decimal point. The bank categorised their customers as either (1) Private Account holders or (2) Business Account holders. The information below summarises customer attitudes towards the quality of service provided by the bank. Use the output to answer the questions below.
a) Briefly describe and compare the distributions of results for the two groups of customers. You should mention appropriate measures of centre and spread, and any other points you feel may be of interest. b) The survey results were described as being symmetrically distributed. What does this mean, and what evidence is there below to support this claim? c) The standard deviation of the ratings for the Private Account holders is 1.336. What does this value mean? d) Verify the value of the standard error of the mean (SE Mean) for the Business Account holders. e) Determine a 90% confidence interval for the true mean of the Business Account holders and interpret the result in the context of the situation.
Descriptive Statistics: Quality
Variable Use N N* Mean SE Mean StDev Minimum Q1 Median Q3
Quality 1 45 0 5.971 0.199 1.336 3.700 4.800 6.000 7.050 2 30 0 8.323 0.172 0.941 6.200 7.675 8.400 9.025
Variable Use Maximum
Quality 1 8.400 2 10.000
Stem-and-Leaf Displays: Quality
Solution:
a) Mean for Business group (8.3) is higher than that for Private group (5.97).
StDev for Private group (1.336) is larger than for Business group (0.941), i.e. there is more variation or less consistency in Private group.
No outliers are evident in either distribution and both seem to be quite
1. Customers of a particular bank rated the service provided by the bank on a scale of one to ten, correct to one decimal point. The bank categorised their customers as either (1) Private Account holders or (2) Business Account holders. The information below summarises customer attitudes towards the quality of service provided by the bank. Use the output to answer the questions below.
a) Briefly describe and compare the distributions of results for the two groups of customers. You should mention appropriate measures of centre and spread, and any other points you feel may be of interest. b) The survey results were described as being symmetrically distributed. What does this mean, and what evidence is there below to support this claim? c) The standard deviation of the ratings for the Private Account holders is 1.336. What does this value mean? d) Verify the value of the standard error of the mean (SE Mean) for the Business Account holders. e) Determine a 90% confidence interval for the true mean of the Business Account holders and interpret the result in the context of the situation.
Descriptive Statistics: Quality
Variable Use N N* Mean SE Mean StDev Minimum Q1 Median Q3
Quality 1 45 0 5.971 0.199 1.336 3.700 4.800 6.000 7.050 2 30 0 8.323 0.172 0.941 6.200 7.675 8.400 9.025
Variable Use Maximum
Quality 1 8.400 2 10.000
Stem-and-Leaf Displays: Quality
Solution:
a) Mean for Business group (8.3) is higher than that for Private group (5.97).
StDev for Private group (1.336) is larger than for Business group (0.941), i.e. there is more variation or less consistency in Private group.
No outliers are evident in either distribution and both seem to be quite