Σ{\displaystyle \Sigma } - This symbol is the Greek letter “sigma. ” In math functions it means to add up a series of whatever follows it. In this formula, the Σ sign means that you will calculate the values that follow in the numerator of the fraction, and add them all together, before dividing by the denominator. [2] X Research source xi{\displaystyle x_{i}} - This variable is read as “x sub i. ” The i subscript represents a counter. It means that you will perform the calculation for each value of x that you have in your data set. xavg{\displaystyle x_{avg}} - The “avg” indicates that x(avg) is the average value of all of your x data points. The average is sometimes also written as an x with a short horizontal line drawn over it. In that style, the variable is read as “x-bar,” but it still means the average of the data set. yi{\displaystyle y_{i}} - This variable is read as “y sub i. ” The i subscript represents a counter. It means that you will perform the calculation for each value of y that you have in your data set. yavg{\displaystyle y_{avg}} - The “avg” indicates that y(avg) is the average value of all of your y data points. The average is sometimes also written as a y with a short horizontal line drawn over it. In that style, the variable is read as “y-bar,” but it still means the average of the data set. n{\displaystyle n} - This variable represents the number of items in your data set. Remember that for a covariance problem, a single “item” is comprised of both an x-value and a y-value. The value of n is the number of pairs of data points, not individual numbers.

x{\displaystyle x} - fill this column with the values of your x-data points. y{\displaystyle y} - fill this column with the values of your y-data points. Be careful to align the y-values with the corresponding x-values. In a covariance problem, the order of the data points and the pairings of x and y are important. (xi−xavg){\displaystyle (x_{i}-x_{\text{avg}})} - Leave this column blank in the beginning. You will fill it with data after you calculate the average of the x-data points. (yi−yavg){\displaystyle (y_{i}-y_{\text{avg}})} - Leave this column blank in the beginning. You will fill it with data after you calculate the average of the y-data points. Product{\displaystyle {\text{Product}}} - Leave this final column blank as well. You will fill it as you go along.

For example, the first data point in the x column is 1. The value to enter on the first line of the (xi−xavg){\displaystyle (x_{i}-x_{\text{avg}})} column is 1-4. 89, which is -3. 89. Repeat the process for each data point. Therefore, the second line will be 3-4. 89, which is -1. 89. The third line will be 2-4. 89, or -2. 89. Continue the process for all the data points. The nine numbers in this column should be -3. 89, -1. 89, -2. 89, 0. 11, 3. 11, 2. 11, 7. 11, -2. 89, -0. 89.

For the first line, therefore, your calculation will be 8-5. 44, which is 2. 56. The second line will be 6-5. 44, which is 0. 56. Continue these subtractions to the end of the data list. When you finish, the nine values in this column should be 2. 56, 0. 56, 3. 56, -1. 44, -2. 44, -2. 44, -3. 44, 1. 56, 1. 56.

On the first row of this data sample, the (xi−xavg){\displaystyle (x_{i}-x_{\text{avg}})} that you calculated is -3. 89, and the (yi−yavg){\displaystyle (y_{i}-y_{\text{avg}})} value is 2. 56. The product of these two numbers is -3. 892. 56=-9. 96. For the second row, you will multiply the two numbers -1. 880. 56=-1. 06. Continue multiplying row by row to the end of the data set. When you finish, the nine values in this column should be -9. 96, -1. 06, -10. 29, -0. 16, -7. 59, -5. 15, -24. 46, -4. 51, -1. 39.

For this sample data set, the sum should be -64. 57. Write this total in the space at the bottom of the column. This represents the value of the numerator of the standard covariance formula.

For this sample problem, there are nine data pairs, so n is 9. The value of (n-1), therefore, is 8.

For this sample data set, this calculation is -64. 57/8, which gives the result of -8. 07.

To simplify your labelling, you could call the third column something like “x difference” and the fourth column “y difference,” as long as you remember the meaning of the data. If you begin your table in the top left corner of the spreadsheet, then cell A1 will be the x label, with the other labels going across to cell E1.

Your x values will begin in cell A2 and will continue down for as many data points as you need. Your y values will begin in cell B2 and will continue down for as many data points as you need.

For example, if you have 100 data points, they will fill in cells A2 through A101, so you will enter =AVG(A2:A101). For the y data, enter the formula =AVG(B2:B101). Remember that you begin a formula in Excel with an = sign.

For the example of 100 data points, the average would be in cell A103, so your formula will be =A2-A103.

For the example of 100 data points, this formula will go into cell E103. You will enter =sum(E2:E102).

For example, at the website http://ncalculators. com/statistics/covariance-calculator. htm, there is a horizontal box for entering x-values and a second horizontal box for entering y-values. You are instructed to enter your terms, separated only by commas. Thus, the x-data set that was calculated earlier in this article would be entered as 1,3,2,5,8,7,12,2,4. The y-data set would be 8,6,9,4,3,3,2,7,7. At another site, https://www. thecalculator. co/math/Covariance-Calculator-705. html, you are prompted to enter your x-data in the first box. Data is entered vertically, with one item per line. Therefore, the entry on this site would look like: 1 3 2 5 8 7 12 2 4

Consider the sample data set that was calculated above. The resulting covariance is -8. 07. The negative sign here means that as the x-values increase, the y-values will tend to decrease. In fact, you can see that this is true by looking at a few of the values. For example, the x-values of 1 and 2 correspond to y-values of 7, 8 and 9. The x-values of 8 and 12 are paired respectively with y-values of 3 and 2.

For the sample data set, the covariance of -8. 07 is fairly large. Notice that the data values range from 1 through 12, so 8 is a pretty high number. This indicates a strong connection between the x and y data sets.

For example, suppose you are comparing shoes sizes against SAT scores. Because there are so many factors that affect a student’s SAT scores, we would expect a covariance score of near 0. This would indicate almost no connection between the two values.

To review plotting points on the coordinate plane, see Graph Points on the Coordinate Plane.