This page is designed to demonstrate the various calculations required for the S1 Statistics module. Students can generate data and see the results of the calculations; also students can try the calculations for themselves and check against the computer's results.

$Y=aX+b$ | |

First Sample: | |

Second Sample: |

First Sample: | |

Second Sample: |

Class Interval | Frequency | ||
---|---|---|---|

First | Second |

(Data rounded to nearest whole number.)

First Leaf | Stem | Second Leaf |
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Mark: | |

Points from first sample below mark: | |

Approximate points from first sample below mark: | |

Points from second sample below mark: | |

Approximate points from second sample below mark: |

First Sample | Second Sample | |
---|---|---|

Mean: The mean of a data set is the sum of the values divided by the number of values. $$\overline{x}=\frac{1}{n}{\sum}_{i=1}^{n}{x}_{i}$$ | ||

Median: The median of a data set is the middle value when they are listed in order. If there are an even number, it is the average of the two middle values. | ||

Modal class: To define the modal class of a data set, the data needs to be divided into classes as in a frequency table. Then the modal class is the class or classes containing the most elements of the data set. Mode: The mode of a data set is the value or values that occur most frequently in the data. | ||

Variance: The variance of a data set is a measure of its spread. It is defined as: $${\sigma}^{2}=\frac{1}{n}{\sum}_{i=1}^{n}({x}_{i}-\overline{x}{)}^{2}$$ (where $\overline{x}$ is the mean) but is more conveniently calculated using the formula: $${\sigma}^{2}=\frac{1}{n}\sum _{i=1}^{n}{x}_{i}^{2}-{\overline{x}}^{2}$$ | ||

Standard Deviation: The standard deviation of a data set is a measure of its spread. It is defined as the square root of the variance. | ||

Lower Quartile: The lower quartile of a data set is the value such that a quarter of the points lie below that value and three-quarters lie above. Its definition is slightly different depending on whether or not there is an actual data point satisfying that property. | ||

Upper Quartile: The upper quartile of a data set is the value such that three-quarters of the points lie below that value and a quarter lie above. Its definition is slightly different depending on whether or not there is an actual data point satisfying that property. | ||

Inter-Quartile Range: The inter-quartile range of a data set is a measure of its spread. It is defined as the upper quartile minus the lower quartile. | ||

Skewness $\frac{3(\overline{x}-median)}{\sigma}$: | ||

Skewness $\frac{\overline{x}-mode}{\sigma}$: | ||

Quartile skewness coefficient: | ||

Estimate of Mean: | ||

Estimate of Variance: | ||

Estimate of Standard Deviation: | ||

Estimate of Median: | ||

Estimate of Lower Quartile: | ||

Estimate of Upper Quartile: | ||

Estimate of Inter-Quartile Range: | ||

Additional quantile calculations: | ||

th quantile of | ||

Estimate: |

$\begin{array}{rl}{S}_{xx}& =3\\ {S}_{yy}& =4\\ {S}_{xy}& =5\\ r=\frac{{S}_{xy}}{\sqrt{{S}_{xx}{S}_{yy}}}& =6\\ Y& =7X+8\end{array}$