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NBA Stats
Mean is determined by adding all data points in a single column together and dividing by the number of data points (in this case, 100). The Excel "AVERAGE" function was used to save time on arithmetic, but performs exactly this calculation.
Median simply takes the central value in a data set when the set is arranged in order of numerical value (or the mean of the two central data points when the data set contains an even number of points). Data was sorted first by height and then by points to determine the median scores for each data set, respectively; the mean of the values in rows 51 and 52 of the spreadsheet (corresponding to the 50th and 51st values in the data set, as row 1 was occupied by the column titles) were taken as the median.
Mode is given simply by frequency; data was again sorted independently for each data set an the most frequent value in each column was determined. Two values had the same highest frequency in the "points" data set (four times each), making this set multimodal (bimodal).
Standard deviation is calculated first by taking the difference of each data point from the mean and squaring the result. Each of these resulting figures is then averaged (i.e. The mean is calculated), and the square root of this number is the standard deviation. The Excel function STDEV was used to save time on arithmetic.
Pearson's Correlation Coefficient is calculated by dividing the covariance of the data sets by the product of the standard deviations. In order to calculate covariance, each pair of data points (i.e. height and the number of points achieved) is combined first by subtracting the expected value of the data point (i.e. The mean) from the value of the data point itself, then multiplying these together. For instance, the first data pair (when sorted by height) is 72 (for height) and 13.1 (for points). Mean height is 78.7 and mean points is 16.843, so calculating the covariance of this data pair would look like this:
(72 -- 78.7)(13.1-16.843) = 25.0781
In order to develop the value for each pair, two new columns were created in the Excel sheet to calculate the difference of the data point and the mean with the following formulas:
=a2-78.7 (for height, pasted into the other 99 rows which automatically adjust the cell value for each row, as =a3-78.7, a4-78.7, etc.), and =b2-16.843 (for points, also pasted).
A third column with the following formula created the product of each row in these two columns:
=c2*d2 (pasted for all rows).
The average function was used to determine the mean of this last row, which is the covariance: 2.1679. Standard deviations are 3.60274867 (for height) and 3.74805687 (for points), meaning Pearson's coefficient is calculated as:
2.1679/(3.60274867 * 3.74805687) = 0.160545859.
Linear regression attempts to find the line of best fit for a data sample. The basic equation of any line for variables x and y is given as y = a + bx. For a linear regression slope (b) is calculated as:
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