Class Notes (1,100,000)

CA (620,000)

McMaster (50,000)

BIOLOGY (2,000)

BIOLOGY 1A03 (900)

Lovaye Kajiura (200)

Lecture 1

This

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1.1 – Statistical Analysis

1.1.1 - State that error bars are a graphical representation of the variability of data

Error bars are a graphical representation of the variability of data. Error bars can be used to

show either the range of data or the standard deviation on a graph. The value extending

above and below one bar will be the same.

When we collect data, it will always variation data because biological systems are subject to

a genetic program and environmental variation.

Time is sometimes too limited to be able to repeat experiments enough time to confirm an

accurate result. Instead, we display data, we show the degree of variability in the readings.

When we are doing this on a graph, we use error bars. Each error bar represents the range

of readings obtained for that value, or the standard deviation.

1.1.2 - Calculate the mean and standard deviation of a set of values

Mean

The mean is a measure of the central tendency of the data. If the distribution is skewed, the

mean may not in fact be the middle value. The median or mode may be more appropriate.

The mean is an average of data points. To calculate a mean value, all the values are

summed, and the total divided by the number of values.

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= arithmetic mean

= sum of all measurements

= the total number of measurements

Standard Deviation

The standard deviation is a measure of how the individual observations of a data set are

dispersed or spread around the mean. Standard deviation is determined by a mathematical

formula which is programmed into your calculator.

The standard deviation of the mean tells us how spread out the readings are. A small

standard deviation indicates that the data is clustered closely around the mean value, whilst

a large standard deviation indicates a wider spread around the mean

To calculate this by hand:

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Once obtained, the value may be applied to the normal distribution curve. Note that 68% of

data occurs within ±1 SD, and more than 95% of the data occurs within ±2 SDs.

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To calculate using the Graphics Calculator (TI-nspire©):

Mean:

Then simply enter the numbers, separated by commas, and press Enter

Standard Deviation:

Then enter the numbers, separated by commas, and press Enter

Mean in Experimental situations

Mean, Median and Mode -

Mode is the most frequent in a set of values

Median is the middle value when in a set of values arranged in ascending order

Mean is the sum of all the values divided by the number of values

Range is the spread of the data, measured by the difference between the highest and

lowest values. This is especially affected by any outliers.

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