Statistics

 Statistics Solver 

Statistics

81. Mean: $\mu =\frac{\sum x_i}{n}$

82. Median: Middle value in a sorted list.

83. Mode: Most frequent value in a dataset.

84. Variance: ${\sigma }^2=\frac{\sum (x_i-\mu {)}^2}{n}$

85. Standard Deviation: $\sigma =\sqrt{{\sigma }^2}$

86. Covariance: $\text{Cov}(X,Y)=\frac{\sum (x_i-{\mu }_x)(y_i-{\mu }_y)}{n}$

87. Correlation Coefficient: $r=\frac{\text{Cov}(X,Y)}{{\sigma }_x{\sigma }_y}$

88. Probability: $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

89. Conditional Probability: $P(A\mathrm{\mid }B)=\frac{P(A\cap B)}{P(B)}$

90. Bayes' Theorem: $P(A\mathrm{\mid }B)=\frac{P(B\mathrm{\mid }A)P(A)}{P(B)}$

91. Binomial Distribution: $P(X=k)=\left(\genfrac{}{}{0px}{}{n}{k}\right)p^k(1-p{)}^{n-k}$

92. Poisson Distribution: $P(X=k)=\frac{{\lambda }^k{e}^{-\lambda }}{k!}$

93. Normal Distribution: $f(x)=\frac{1}{\sigma \sqrt{2\pi }}{e}^{-\frac{(x-\mu {)}^2}{2{\sigma }^2}}$

94. Z-Score: $z=\frac{x-\mu }{\sigma }$

95. Chi-Square Test: ${\chi }^2=\sum \frac{(O_i-E_i{)}^2}{E_i}$

96. T-Test: $t=\frac{\bar{x}-\mu }{s\mathrm{/}\sqrt{n}}$

97. F-Test: $F=\frac{{\sigma }_1^2}{{\sigma }_2^2}$

98. Regression Line: $y=mx+b$

99. Coefficient of Determination: $R^2=\frac{\text{Explained Variation}}{\text{Total Variation}}$

100. Standard Error: $SE=\frac{\sigma }{\sqrt{n}}$