Two Variable Statistics Calculator

Data Input



XY
Count\(n=5\)
Sum\(\sum{x_i}=25\)
Mean (Average)Mean (Average): \[\overline{x}=\frac{\sum{x_i}}{n}\]\(\overline{x}=5\)
Minimum\(min=1\)
Q1\(Q_1=2\)
Median(Q2)\(Q_2=5\)
Q3\(Q_3=8\)
Maximum\(max=9\)
RangeRange: \[Range=Max-Min\]\(Range=8\)
Interquartile RangeInterquartile Range: \[IQR=Q3-Q1\]\(IQR=6\)
ModeMode: The most frequently occurring number(s)Mode: No Mode
Outlier(s)Outlier(s): Any numbers less than \[Q1-1.5\cdot IQR\] or greater than \[Q3+1.5\cdot IQR\]{ }
Corrected Sum of Squares\(\sum x^2=165\)
Corrected Sum of SquaresCorrected Sum of Squares: [S_{xx}=\sum{(x_i-\overline{X})^2}\]\(S_{xx}=40\)
(Sample) Variance(Sample) Variance \[s^2=\frac{\sum{(x-\overline{x}_i)^2}}{n-1}\]\(s^2=10\)
(Sample) Standard Deviation(Sample) Standard Deviation: \[s=\sqrt{\frac{\sum{(x-\overline{x}_i)^2}}{n-1}}\]\(s=3.1622776601684\)
(Population) Standard Deviation(Population) Variance: \[\sigma^2=\frac{\sum{(x-\overline{x}_i)^2}}{n}\]\(\sigma^2=8\)
(Population) Standard Deviation(Population) Standard Deviation: \[\sigma=\sqrt{\frac{\sum{(x-\overline{x}_i)^2}}{n}}\]\(\sigma=2.8284271247462\)
Count\(n=5\)
Sum\(\sum{y_i}=30\)
Mean (Average)Mean (Average): \[\overline{y}=\frac{\sum{y_i}}{n}\]\(\overline{y}=6\)
Minimum\(min=2\)
Q1\(Q_1=3\)
Median(Q2)\(Q_2=6\)
Q3\(Q_3=9\)
Maximum\(max=10\)
RangeRange: \[Range=Max-Min\]\(Range=8\)
Interquartile RangeInterquartile Range: \[IQR=Q3-Q1\]\(IQR=6\)
ModeMode: The most frequently occurring number(s)Mode: No Mode
Outlier(s)Outlier(s): Any numbers less than \[Q1-1.5\cdot IQR\] or greater than \[Q3+1.5\cdot IQR\]{ }
Corrected Sum of Squares\(\sum y^2=220\)
Corrected Sum of SquaresCorrected Sum of Squares: \[S_{yy}=\sum{(y_i-\overline{Y})^2}\]\(S_{yy}=40\)
(Sample) Variance(Sample) Variance: \[s^2=\frac{\sum{(y-\overline{y}_i)^2}}{n-1}\]\(s^2=10\)
(Sample) Standard Deviation(Sample) Standard Deviation: \[s=\sqrt{\frac{\sum{(y-\overline{y}_i)^2}}{n-1}}\]\(s=3.1622776601684\)
(Population) Standard Deviation(Population) Variance: \[\sigma^2=\frac{\sum{(y-\overline{y}_i)^2}}{n}\]\(\sigma^2=8\)
(Population) Standard Deviation(Population) Standard Deviation: \[\sigma=\sqrt{\frac{\sum{(y-\overline{y}_i)^2}}{n}}\]\(\sigma=2.8284271247462\)
Two-Variable Statistics
Box-and-Whisker Plot (Include Outliner)
Sum of Cross Products\(\sum xy=190\)
Corrected Sum of Cross ProductsCorrected Sum of Cross Products: \[S_{xy}=\sum{(x_i-\overline{X})(y_i-\overline{Y})}\]\(S_{xy}=40\)
CovarianceCovariance: \[\text{cov}(X,Y)=\frac{\sum{(x_i-\overline{X})(y_i-\overline{Y})}}{n}\]\(\text{cov}(X,Y)=8\)
Correlation CoefficientCorrelation Coefficient: \[r=\frac{\text{cov}(X,Y)}{\sigma_x\cdot\sigma_y}\]\(r=1\)
Coefficient of Determination\(r^2=1\)
Line of Best Fit\(y = x + 1\)
Residual plot

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