##### Biometry Chapter 3

Descriptive Statistics

Statistics that summarize the main characteristics of a sample of data

Three types of descriptive statistics

1. Sample size (n)

2. Measures of central tendency

3. Measures of variability

Measures of central tendency

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

Three measures of central tendency

1. Mean

2. Median

3. Mode

Mean

The average number of a sample

- Affected by extreme values

Median

The midpoint of a sample

- Less sensitive to extreme values

Mode

Number that occurs the most in a sample

- Not affected by extreme values

Measures of variability

Measures that summarize how similar the data in a sample are

Four measures of variability

1. Range

2. Interquartile range

3. Variance

4. Standard deviation

Range

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

- Sensitive to extreme values

Interquartile range

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

- Not very sensitive to extreme values

Variance

The mean squared deviation from the mean

Sum of squares

The sum of the squared deviations from the mean

Degrees of freedom

1 less than the sample size.

n-1

Standard deviation

The square root of the variance

Frequency distributions

Show how many times different values occur in a sample

- table, graph, or histogram

1. Tail

2. Body

1. The extremes of a normal distribution

2. The middle section of the bell shaped curve

Parametric statistics

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

Pie Chart

Chart showing the frequencies of a sample

Box Plot

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

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

Error bars

Mean + standard deviation

Mean - standard deviation

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

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

What are 4 types of distributions?

Normal

Binomial

Poisson

Uniform

What is a normal distribution?

A bell shaped frequency distribution with a tail and a body

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

- No skew to the data

- Both tails go on for infinity

Binomial statistics

Collecting data from two nominal categories

- heads or tails

- dead or alive

- male or female

Poisson Statistics

Counting data that are whole numbers

- Number of eggs in a nest

- Number of cells in a petri dish