Requirements Lab book Text book Standard deviation little sheet Big sheet Scientific calculators

Statistics in AS biology Lab books Text p 255

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Requirements Lab book student guide print off Highlighter Standard deviation instruction sheet Standard deviation question sheets Text p 255- the only ‘maths’ bit not in the maths section at the end of the book Optional Callipers and 2 bean populations, french and runner

Student practical guide (section – F) page 20

We use n-1 as we are calculating SD for a sample of data We use n-1 as we are calculating SD for a sample of data. Care when using calculator as these often use n instead

Standard deviation Maths standard deviation The formula (n or n-1) Alternative method = square each piece of data and add them up, divide this by the number of pieces of data and then subtract the mean squared. Find the square root of the answer

Standard deviation notes SEE STUDENT TYPED SHEET This is a measure of the spread of the data around the mean; the larger the standard deviation the larger the spread. In a normally distributed set of data (which we can assume to be the case for the needs of A level biology) 95% of the data points lie within 2 standard deviations either side of the mean. Why not just use the RANGE? The standard deviation is not overly influenced by outlying values, (it is more representative of the spread) also only valid if done on 5 or more data

Range and Standard deviation for measuring Variation A and B show TWO different cases where twenty measurements were taken and a mean calculated. The blue circles Represent the data values either side of the mean (solid line). < x > A 10 15 5 B A B A B Range Standard Deviation

Plotting standard deviation error bars One SD above and below = 68% of the data Two standard deviations above and below = 95% of the data

SD and the ‘Normal Distribution’ x - x - - 1 SD x - + 1 SD Mean ± 1 SD = 68% of variation Mean ± 2 SD = 95% of variation

Do question 1 on the worksheet The one about bubbles

Rate of reaction / bubbles per minute Answers Temperature / °C Rate of reaction / bubbles per minute mean SD  0  3.0  1.0  6.0  5.0 3.6 1.95  5 15.0 13.0 12.0 13.6 1.34 10 20.0 23.0 24.0 16.0 21.0 20.8 3.11 15 22.0 14.0 31.0 7.52 20 26.0 32.0 36.0 39.0 32.8 4.97

Using excel (add to your sheet) Select a new cell Press= Type SD (for standard deviation) Scroll down to standard deviation for a sample (STDEVA) Highlight the cells with the data you want to do the SD on Press close brackets ) Hit =

Standard deviation – NOW USE YOUR CALCULATOR TO CHECK IF THIS WORKS… Show and tell how to use your calculator to calculate standard deviation Set the mode stats(2) 1 (1 variable) values type + = press AC shift 1 4 (mean) 2 (SD)

FINISH THE SHEET

1c The mean, at 5 °C is the most reliable/at 15 °C is the least reliable. (1 mark) Because SD is smallest at 5 °C/ largest at 15 °C. (1 mark) Data at 5 °C are less spread/have less variation/are less dispersed from the mean/ORA. (1 mark)

1d Mean = 13.6 Standard deviation = 1.34 14.94 12.26

Results of each repeat done mean 2b Student Results of each repeat done mean  sd 1 14.0 23.0 9.0   15.3  n/a 2 17.0 19.0 27.0 20.0 31.0  22.8 5.93 3 24.0 18.0 21.0 29.0 26.0 4.26 4 25.0 22.0 2.92 5 22.8 2.39

2c The true mean is (close to) 22.8; All students with five or more repetitions succeed in getting an accurate mean / 3 repititions not sufficient As the number of repeats increases the standard deviation becomes smaller until 8 repeats where more repeats does not decrease the SD by much (decreases then levels out) Outliers affect sd less than a range Error bars become smaller as the number of repeats increase Students 4 and 5 will be able to plot the points with the greatest certainty.

SD and the ‘Normal Distribution’ x - x - - 1 SD x - + 1 SD Mean ± 1 SD = 68% of variation Mean ± 2 SD = 95% of variation

Text page 255 Most maths at the back except for this!!

Measuring variation extension (I did not get on to this) 1 calliper each Measure the length of 1 French bean and 1 runner bean between a pair Each person measures the maximum length of one bean with your ruler Are they different from each other? How can we improve the precision of the measurement? Calliper

Using a Vernier calliper Main scale (ignore – in inches) Auxillary scale What the calliper should look like at zero

make a note of where the first mark on the auxiliary scale falls on the main scale (between 12 mm and 13 mm) The last digit (tenths of a millimeter) is found by noting which line on the auxiliary scale coincides with a mark on the main scale (the last digit is 3 because the third auxiliary mark lines up with a mark on the main scale. Therefore, the length of the object is 12.3 mm.)

Calculate the mean and standard deviation for each variety of bean

Conclusions Plot a bar graph (include the mean as a bar and the 2SD above and below as an error bar) Add bars to show 2 SD above and 2 SD below the mean. This shows where OVER 95% of the data are spread Which type of bean shows the most intraspecific variation? mean + 2 x SD mean - 2 x SD

SE

Example calculations Maths skills for A level biology Summary questions p25