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