Title: Averaging Data
Course: BTEC-2000-301-302-303-F21 > Section: InnovaBio® Project Presentation

The previous learning activity asks you to find the average of data from batch records.  The following series of learning activities describes how to find an average using the spreadsheet program Microsoft Excel.

Finding the average is probably something you have encountered before. It is simply adding up all the data points and dividing by the total number of data points. For example, the data set might include the mass in grams of ripe roma tomatoes: 72, 42, 35, 51, 63, 45, 81, 49, 55, and 66. There are 10 data points so you add up all the numbers and divide by 10.

72 + 42 + 35 + 51 + 63 + 45 + 81 + 49 + 55 + 66 = 55.9g

10

There are a few ways to represent the formula for calculating the average mathematically. In the formulas below, X¯X ¯is the symbol used to indicate average. 𝑥 is for the data values. 𝑥_1, 𝑥_2,...𝑥_n, and 𝑥_i all indicate specific data points: the first data point (72 above) is 𝑥_1 , the second data point (42) is 𝑥_2 and so on until you include all data points in the set of “n” values. For the given data set, n = 10 and 𝑥_n = 66. As you can see, the formula between the two equal signs (below) looks very similar to the equation above. The rightmost  formula below is just another way to represent average. The equation is still divided by n (1/n). The Greek symbol 𝚺 (sigma) tells you to take the sum of the 𝑥 values (𝑥_i) starting with the first (i=1 below the 𝚺). The n above the 𝚺 indicates the number of data values included in the  set.

Here again is the Roma tomato average mass for the data set: 72, 42, 35, 51, 63, 45, 81, 49, 55, and 66.