Biometry Chapter 3

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1

Descriptive Statistics

Statistics that summarize the main characteristics of a sample of data

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Three types of descriptive statistics

1. Sample size (n)

2. Measures of central tendency

3. Measures of variability

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Measures of central tendency

Measures that summarize what the data in a sample are typically like.

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Three measures of central tendency

1. Mean

2. Median

3. Mode

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Mean

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The average number of a sample

- Affected by extreme values

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Median

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The midpoint of a sample

- Less sensitive to extreme values

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Mode

Number that occurs the most in a sample

- Not affected by extreme values

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Measures of variability

Measures that summarize how similar the data in a sample are

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Four measures of variability

1. Range

2. Interquartile range

3. Variance

4. Standard deviation

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Range

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The difference between the smallest and largest values of a sample measuring the spread.

- Sensitive to extreme values

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Interquartile range

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The difference between the lower and upper quartile ranges of a sample.

- Not very sensitive to extreme values

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Variance

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The mean squared deviation from the mean

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Sum of squares

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The sum of the squared deviations from the mean

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Degrees of freedom

1 less than the sample size.

n-1

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Standard deviation

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The square root of the variance

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Frequency distributions

Show how many times different values occur in a sample

- table, graph, or histogram

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Normals distribution

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A bell shaped frequency distribution with a tail and a body

- 95% of the curve falls within 2 standard deviations of the mean

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1. Tail

2. Body

1. The extremes of a normal distribution

2. The middle section of the bell shaped curve

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Parametric statistics

Statistics that rely heavily on the special properties of the normal distribution.

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Binomial statistics

Collecting data from two nominal categories

- heads or tails

- dead or alive

- male or female

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Poisson Statistics

Counting data that are whole numbers

- Number of eggs in a nest

- Number of cells in a petri dish

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Pie Chart

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Chart showing the frequencies of a sample

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Box Plot

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How do you know if you have outliers on a box and whisker plot?

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Max value = UQ + (1.5 x IQR)

Min Value = LQ - (1.5 x IQR)

Any value above or below the max and min are outliers

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Error bars

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Mean + standard deviation

Mean - standard deviation

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On a graph where do the independent and dependent variables go?

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What do the following axis labels mean?

1. Frequency

2. Relative frequency

1. The number of occurrences in a sample

2. The percent of occurrences in a sample