SE Unit 0 Topic 2 Statistics

Introduction to Statistics in AP Biology

• Statistics is crucial for analyzing data in scientific studies.

• Scientists typically collect data from a sample of a population to infer about the general population.

Graphing Data and Distribution

• The first step in data analysis involves graphing the data and examining its distribution.

• Typical data often exhibit a normal distribution, represented as a bell-shaped curve.

Central Tendencies

Measures of Central Tendencies

• Descriptive statistics allow researchers to describe and quantify differences between data sets.

• The center of a distribution can be summarized using three measures: mean, median, and mode.

Mean

• The mean is defined as the average of a data set.

• To calculate the mean, sum all data points and divide by the total number of points.

• Formula: Mean = (Sum of all data points) / (Total number of data points)

Example: Mean Calculation

• In a biology class, students planted five tomato seeds and measured their heights in mm: 65, 52, 71, 56, 61.

• To find the mean, calculate:

  • Mean = (65 + 52 + 71 + 56 + 61)/5 = 61.

Median

• The median is the middle number in a sorted list of data points.

• To find the median, arrange the data in order and identify the middle value.

• If the number of data points is even, average the two middle numbers.

• The median is helpful in data sets with extreme values since it isn’t skewed by extreme measurements.

Example: Median Calculation

• For nine labrador retrievers, the times are measured as: 4, 5, 2, 1, 4, 8, 4, 7, 1.

• Arranging: 1, 1, 2, 4, 4, 4, 4, 5, 7, 8.

• The median is 4.

Mode

• The mode is the value that occurs most frequently in a data set.

• It is less common to use mode for central tendency but is useful in certain distributions, such as bimodal distributions.

Example: Mode Calculation

• For the dataset of 10 high school students’ TikTok usage: 10, 5, 5, 8, 5, 2, 5, 4, 4, 3.

• The mode is 5 since it appears most frequently.

Variability

Measure of Variability

• Variability indicates how spread out a data set is from the central tendency, measured by range and standard deviation.

Range

• Range is calculated as the difference between the largest and smallest values in a dataset.

• A larger range signifies greater variability, while a smaller range indicates less variability.

Example: Range Calculation

• For tomato plants with heights: 65, 52, 71, 56, 61.

• Range = 71 - 52 = 19.

Standard Deviation

• Standard deviation measures how data points deviate from the mean.

• A low standard deviation indicates data points are close to the mean, while a high standard deviation implies a wide spread.

• Standard deviation calculations involve determining the mean, calculating deviations from the mean, squaring those deviations, and then averaging them.

Example: Standard Deviation

• From the tomato plant heights, calculate the mean and deviations.

• After following the standard deviation steps, the resulting standard deviation is calculated as 7.45.

Interpretation of Standard Deviation

• 1 standard deviation encompasses 68% of the data around the mean.

• 2 standard deviations include 95%, and 3 standard deviations include 99% of the data.

Standard Error of the Mean (SEM)

• Standard error of the mean (SEM) provides an estimate of how well the sample mean represents the population mean.

• Lower SEM indicates higher confidence in the mean estimate.

• Formula: SEM = Standard Deviation / Square Root of Sample Size.

Practice with SEM

• Using the tomato plant data with standard deviation of 7.45 and a sample size of 5 yields:

• SEM = 7.45 / √5 = 3.3.

Graphing SEM

• SEM is commonly represented with error bars in graphs, indicating the range of variability in the mean estimate.

• If error bars overlap, the observed difference may not be statistically significant.

Conclusion

• Analyzing measures of central tendency and variability are crucial for interpreting data effectively in AP Biology.