Mean, Median, and Mode
The mean is the average, or the sum of the data divided by the number of data items. The middle number in a set of ordered data is called the median. The mode is the number that appears most often in a set of data.
Example
A scientist counted the number of distinct songs sung by seven different male birds and collected the data shown below.
To determine the mean number of songs, find the sum of the songs sung by all the male birds and divide by the number of male birds.
To find the median number of songs, arrange the data items in numerical order and identify the number in the middle.
27 28 29 35 36 36 40
The number in the middle is 35, so the median number of songs is 35.
The mode is the value that appears most frequently. In the data, 36 appears twice, while every other item appears only once. Therefore, 36 is the mode.
Estimation
An estimate is a reasonable approximation of a numerical value. Estimates are made based on careful assumptions and known information.
Scientists use estimates in biology for two primary reasons: when an exact count or calculation cannot be made or is impractical to make, and to make reasonable approximations of answers that will be calculated or measured later.
One method for estimation used in biology is sampling. In sampling, the number of organisms in a small area (a sample) is multiplied to estimate the number of organisms in a larger area.
Example
Follow these steps to use sampling to estimate the total number of birds in the photo.
Count the birds in the highlighted area of the photo. In the highlighted area of the photo, there are 36 birds.
Determine the portion of the entire photo represented by the highlighted area. In this case, the highlighted area is 1/6 of the total area.
Calculate your estimate by multiplying the number of birds in the sample area by 6 (because the entire photo is 6 times as large as the sample area). A reasonable estimate of the total number of birds is 36 × 6, or 216 birds.
HINT: Estimates and calculated answers are rarely exactly the same. However, a large difference between an estimated answer and a calculated answer indicates there may be a problem with the estimate or calculation.
Table of Contents
- Formulas and Equations
- Applying Formulas and Equations
- Mean, Median, and Mode
- Estimation
- Using Measurements in Calculations
- Effects of Measurement Errors
- Accuracy
- Precision
- Comparing Accuracy and Precision
- Significant Figures
- Calculating With Significant Figures
- Scientific Notation
- Calculating With Scientific Notation
- Dimensional Analysis
- Applying Dimensional Analysis