Cambridge Technicals Level 3 Applied Science Unit 3 Lesson Element - 1 Variance and Standard

Lesson Element

Unit 3: Scientific analysis and reporting

LO1: Be able to use mathematical techniques to analyse data

Variance and Standard Deviation

Instructions and answers for tutors

These instructions cover the learner activity section which can be found on page 4. This Lesson Element supports Cambridge TechnicalsLevel 3 in Applied Science.

When distributing the activity section to the learners either as a printed copy or as a Word file you will need to remove the tutor instructions section.

The activity

Variance and standard deviation are statistical techniques that are used to determine how spread out a set of data is from the mean value. They are often used to determine the quality of a set of data.

In these two activities, learners will determine the variance and standard deviation for sets of data. In Activity 1, the problem involves a sample set of data and in Activity 2 a set of data representing the population.

Both activities provide the opportunity for developing ICT skills by solving the problems using a spreadsheet.

Learners will require access to the Excel spreadsheet:
Standard Deviation Problems Data

Suggested timings

Activity 1: 45 minutes

Activity 2: 45 minutes

Version 21© OCR 2018

Activity 1

To note – this problem involves sample data. The formula for variance and standard deviation must take account of this with N  1 being used.

The solutions to this problem have been calculated with the aid of a spreadsheet. Learners could calculate solutions manually, or could use ICT to develop a solution.

Part a

Mean Blood Pressure = 1464 / 18 = 81.3 mm Hg

Part b

Variance 2 = average or the squared differences from the mean = 1788 / (18  1)

Note: for sample data N = N – 1 i.e. 18 – 1

Variance 2 = 105.2 mm Hg

Part c

Standard deviation

Standard deviation =  variance = 105.2 = 10.3 mm Hg

Part d

1SD higher than mean = 81.3 + 10.3 = 91.6 mm Hg

1SD lower than mean = 81.3 – 10.3= 71.1 mm Hg

In order to pass the blood pressure readings must be in the range 71.1 mm Hg to
91.6 mm Hg.

For the sample ... 4 out of 18 blood pressure readings fail.

Part e

4/18 × 100% = 22% blood pressure readings fail.

This means that a more detailed study should be conducted.

Tutors could develop similar example problems.

Activity 2

To note – this problem involves population data. The formula for variance and standard deviation must take account of this with N being used.

The solutions to this problem have been calculated with the aid of a spreadsheet. Again, solutions could be determined manually or using ICT.

Part a

Mean concentration = 200/20 = 10.0 mol dm-3

Part b

Variance 2 = average or the squared differences from the mean = 1.32 / 20

Note: for population data N = N i.e. 20. Variance 2 = 0.07

Part c

Standard deviation

Standard deviation =  variance = 0.07 = 0.26 mol dm-3

Part d

2SD higher than mean = 10.0 + (2 × 0.26) = 10.52 mol dm-3

2SD lower than mean = 10.0 – (2 × 0.26) = 9.48 mol dm-3

In order to pass quality control all concentration readings must be in the range 9.48 mol dm-3 to10.52 mol dm-3.

For the population data all values are in the range, and so the batch of sulfuric acid passes.

Tutors could develop similar example problems.

Version 21© OCR 2018

Lesson Element

Unit 3: Analytical Techniques

LO1: Be able to use mathematical techniques to analyse data

Learner Activity

Variance and Standard Deviation

In these two activities, you will determine the variance and Standard Deviation for sets of data. In Activity 1, the problem involves a sample set of data and in Activity 2 a set of data representing the population. You will need to carefully select the correct formula to use for each activity.

Both activities provide you with the opportunity to develop your skills in using a spreadsheet to solve problems.

Activity 1

A doctor’s practice carries out a small-scale study of the diastolic blood pressure of patients in a particular age group.

During a one-week period they take a sample of the blood pressure readings of 18 patients. The sample is believed to be representative of all of the patients in this age group registered with the practice. Here are the measured diastolic blood pressures (mm Hg):

72 / 79 / 105 / 85 / 76 / 73 / 99 / 84 / 100
75 / 75 / 74 / 68 / 83 / 82 / 80 / 78 / 76

The lead nurse at the practice wishes to conduct a more detailed study if more than 10% of the blood pressure readings are greater than one standard deviation (1SD) away from the mean.

(a)Determine the mean for the sample.

(b)Determine the variance.

(c)Determine the standard deviation.

(d)Identify all blood pressure readings in the sample that are greater than 1SD from the mean.

Determine the percentage of blood pressure readings that are greater than 1SD from the mean, and if a more detailed study should be conducted.

Activity 2

During the production of sulfuric acid in a chemical plant, the population data for 20 readings of sulfuric acid concentration (mol dm-3) is as follows:

9.8 / 9.7 / 9.9 / 10.1 / 10.2 / 9.5 / 10.3 / 10.4 / 9.6 / 9.6
10.3 / 10.2 / 10.2 / 9.8 / 9.9 / 10.2 / 10 / 10 / 10.1 / 10.2

The processing of the sulfuric acid batch requires that none of the readings are more than two standard deviations (2SD) from the mean.

(a)Determine the mean for the population.

(b)Determine the variance.

(c)Determine the standard deviation.

Identify if any of the readings are more than 2SD from the mean and if the batch passes or fails.