S1 - Statistics

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.

Data Definintion

First Data Sample

Second Data Sample

Y=aX+b

Raw Data

First Sample:
Second Sample:

Sorted Raw Data

First Sample:
Second Sample:

Data Representation

Frequency Table

Class Interval Frequency
First Second

Stem and Leaf Diagram

(Data rounded to nearest whole number.)

First Leaf Stem Second Leaf

Histogram

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:

Boxplot

Sample Statistics

First Sample Second Sample
Mean: The mean of a data set is the sum of the values divided by the number of values. x¯=1n i=1 nx 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: σ 2=1n i=1 n(x ix¯) 2 (where x¯ is the mean) but is more conveniently calculated using the formula: σ 2=1n i=1 nx i 2x¯ 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 3(x¯median)σ:
Skewness x¯modeσ:
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:

Correlation

S x x = 3 S y y = 4 S x y = 5 r=S xyS xxS yy = 6 Y = 7 X + 8