Maths

Many manufacturing processes produce items that vary slightly in some way (dimensions, mass, resistance etc.) but are generally within certain limits. Repeated physical measurements of sample items tend to follow what is called a normal distribution about the average or mean value. Variations can be due to the manufacturing processes or the measurement process.

**Available downloads**

The full lessons along with a supporting toolkit are available in three different formats,
A4, A3 and as a Powerpoint deck.

Download Lesson Kit

Contains the full lesson along with a supporting toolkit, including teachers’ notes.

If, however, 99.99% of the products are perfect then to have a better than 50:50 chance of detecting at least one defective item, almost 7000 samples would need to be checked! (1 − 0.99996932 = 50.004%).

- 1. variations in the manufacturing process(es)

- 2. variations in the measurement process.

- The average of a set of values is called the mean. true
- The sum of the deviations from the mean is zero. true
- The sum of the absolute deviations from the mean is called the standard deviation. false
- About 95% of a set of data that has a normal distribution will be within 2 standard deviations of the mean. true
- A 99% confidence level means that if the test were repeated many times 99% of them would give the same result. true
- A confidence level is also called a ‘margin of error’. false
- A ‘confidence interval’ is the range of values that contains the true value, at the specified confidence level. true
- The main stages in drug development are discovery, production and approval. false
- In a double blind test neither the patients nor the researchers know who receives the product being tested. true
- Drug development usually takes about one year. false

- absolute value
- the numerical value of a number, ignoring any leading minus sign
- confidence interval
- the interval around an estimate which includes the margin of error above and below the estimate
- double-blind test
- a test in which neither the participants nor the researchers know which participants belong to the control group
- histogram
- a graphical representation of sample data using bars of different heights with no gaps between them
- level of confidence
- the probability that an estimate is correct; in the case of random samples the level of confidence depends on the sample size: e.g. for 99% level of confidence the margin of error is approximately 1.29(√n)
- margin of error
- the range above and below an estimate in which one is confident that the true value lies; e.g. 55% +/- 2%
- mean
- the average
- normal distribution
- when many random samples of a measurement are made they tend to be distributed about the mean in a mathematically predictable way; sometimes called a 'bell curve'
- objective
- without bias; opposite to subjective
- pH
- a measure of the acidity or basicity of an aqueous solution; pH values are generally in the range 0 to 14, where 0 is a strong acid, 7 is neutral and 14 is a strong base. Negative values are possible; commercial HCl has a pH of about -1.1. Saturated NaOH has a pH of about 15.
- pharmaceutical
- relating to the production of medicines
- placebo
- an ineffective treatment that the patient assumes to be effective
- production line
- a manufacturing process in which a product is made in a sequence of steps, typically in adjoining locations
- random sample
- a sample that is not selected for any particular reason
- reagent
- a substance that takes part in a chemical reaction
- standard deviation
- a measure of how sample measurements are clustered around the mean; it is equal to the square root of the variance
- variance
- a measure of how sample measurements are clustered around the mean; it is equal to the square of the standard deviation