1. ‘Statistics can prove anything’

‘Figures cannot lie’

Comment on the above two statements, indicating reasons for the existence of such divergent views regarding the nature and functions of statistics.

2. From the following data compute quartile deviation and the coefficient of skewness:

Size	5 – 7	8 – 10	11 – 13	14 – 16	17 – 19
Frequency	14	24	38	20	4

3. A bank has a test designed to establish the credit rating of a loan applicant. Of the persons, who default (D), 90% fail the test (F). Of the persons, who will repay the bank (ND), 5% fail the test. Furthermore, it is given that 4% of the population is not worthy of credit; i.e., P(D) = .04. Given that someone failed the test, what is the probability that he actually will default (When given a loan)?

4. Strength tests carried out on samples of two yarns spun to the same count gave the following results:

	Number in sample	Sample Mean	Sample variance
Yarn A	4	50	42
Yarn B	9	42	56

The strengths are expressed in pounds. Does the difference in mean strengths indicate a real difference in the mean strengths of the yarn?

Well produced statistics should have all definitions reported including any assumptions made. Any issues with the quality of the data should also be reported in a transparent manner. If done correctly, the statistics produced are beyond reproach and will serve their purpose, that is, to inform. In this context the figures cannot lie. It is the job of a statistician/analyst to ensure that everything from sampling, data collection and analysis are carried out correctly and without bias. Well produced statistics can inform how resources should be allocated (money to local government), how effective a new drug is and give measures of production quality (say in a biscuit factory) amongst other things. 

However, there are many cases where statistics are misused and/or are produced with bias or errors. The misuse and 'fiddling' of statistics has led to much of the public to have distrust in statistics. This view point is also borne out of ignorance of statistics and how they are produced. The first thing I do when someone quotes statistics is ask what the source is and other probing questions. It is important to approach statistics with a critical mind in order to look for any weaknesses. 

There is always going to be a subjective element to the interpretation of descriptive statistics. Humans are 'programmed' to look for patterns which can sometimes mean that someone will look for patterns in the data that they expect to see due to preconceived ideas they have. A company that has invested a lot of money in a product will not want to find out their is a lack of evidence to suggest that the product does what it says. As long as there is no pressure (including political or commercial) on the statisticians or analysts producing the analyses to be anything but objective then we can have confidence in the figures produced.

Going back to the comment about "statistics can prove anything". Say you were wishing to poll people on their opinions on parenting. The wording of the question is key and this WILL influence the answers that respondents give to the survey. If I worked for the education department and wanted to show that people agreed with cuts I wished to make to primary educational funding then asking a leading question that would likely give me a negative response would be the way forward. This would be how I could use "statistics to prove anything". Also, by only asking people with no children (and thus people who are less likely to consider primary education), I deliberately introduce bias into my sample as it will not represent the population of interest. Anyone carrying out a critique of the survey's methodology would likely pick up any badly designed questions leading to this bias but by that point it may be too late - the newspapers will have moved on to other headlines and the cuts may have already been made.