Statistics
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Statistical data can by typed in by hand, or imported as a text file. This makes it possible to use data from the internet or data logging devices connected to temperature probes and the like.

Here are the options available for graphing and calculating statistics in Maths Helper Plus...

Data Tables

You decide what columns to include in your data table. You can click buttons to plot cumulative frequency or cumulative percentage values.

This table has all possible columns shown:

x  f  x²Â  fx   fx²Â  cum.f  cum.%  rel.f      z score
1  2  1   2    2    2      6.452  0.0645161  -1.7599
2  3  4   6    12   5      16.13  0.0967742  -1.25938
3  5  9   15   45   10     32.26  0.16129    -0.758855
4  6  16  24   96   16     51.61  0.193548   -0.258333
5  6  25  30   150  22     70.97  0.193548   0.242188
6  4  36  24   144  26     83.87  0.129032   0.742709
7  2  49  14   98   28     90.32  0.0645161  1.24323
8  2  64  16   128  30     96.77  0.0645161  1.74375
9  1  81  9    81   31     100    0.0322581  2.24427
totals:
   31 140 756  1

 

Calculations

The following statistics calculated, and all working steps are displayed if required:

mode, mean, median, range, 
sample standard deviation, sample variance,
population standard deviation, population variance,
five number summary with outliers rejected,
inter quartile range.

Here are the working steps displayed by Maths Helper Plus for some sample statistics:

MODE = score with the highest frequency
There are 2 modal scores with f = 6:
   x = 4
   and 5

MEAN = sum of scores / number of scores
     = sum of 'fx' / sum of 'f'
     = 140 / 31
     = 4.51613

MEDIAN = middle score
 n = 31, which is ODD
 So the median is at position (31+1)/2 = 16.
 The median score = 4

RANGE = maximum score - minimum score
      = 9 - 1
      = 8

STANDARD DEVIATION
 sd (population) = sqrt[ (sum of fx²/n) - (sum of fx)/n)² ]
                 = sqrt[ (756/31) - (140/31)² ]
                 = 1.99792

VARIANCE
 var (population) = (sum of fx²/n) - (sum of (fx)/n)²
                  = (756/31) - (140/31)²
                  = 1.99792

FIVE NUMBER SUMMARY (Tukey's Method)
 Step 1: Find the median: Q2
 (See the 'median' option for this procedure)
 Q2 = 4
 There are 31 values, which is an ODD number.
 Split the data into two halves, each including the median.
 Q1 is the median of the lower half,
 and Q3 is the median of the upper half.

Step 2: Find the first quartile: Q1
 There are 16 scores less or equal to the median.
 This is an EVEN number, so Q1 is the average of scores
 at positions: 16/2 = 8 and 8 + 1 = 9.
 The score at position 8 is x = 3,
 and the score at position 9 is x = 3.
 So Q1 = [3 + 3]/2
           = 3

Step 3: Find the third quartile: Q3
There are also 16 scores greater or equal to the median.
so Q3 is the average of scores
at positions: 16 + 16/2 = 24 and 24 + 1 = 25.
The score at position 24 is x = 6,
and the score at position 25 is x = 6.
So Q3 = [6 + 6]/2
          = 6

Step 4: Find the minimum and maximum acceptable scores
[Scores more than 1.5 times the interquartile range (IQR)
below Q1 or above Q3 are rejected as outliers.]
1.5 × IQR = 1.5 × 3 = 4.5
so the lowest acceptable score = 3 - 4.5 = -1.5,
and the highest acceptable score = 6 + 4.5 = 10.5
Rejecting scores outside these limits:
min = 1, Q1 = 3, Q2 = 4, Q3 = 6, max = 9

INTERQUARTILE RANGE = Q3 - Q1
= 6 - 3
= 3

 

Classes

Specify class intervals to apply to your raw data by typing three numbers in the white edit boxes of this dialog box:

 

Once applied to your data, all statistical calculations use the class midpoint values only. Classes are also included in the data tables.

Histogram, Frequency Polygon

There are an incredible range of options for displaying histograms and frequency polygons:

Stem & Leaf, Box & Whisker

Maths Helper Plus provides a comprehensive range of options for creating 'Stem-and-leaf' and box plots. 
This dialog box is used to select the required options:

Here is a stem & leaf plot created with Maths Helper Plus:

STEM AND LEAF PLOT:
Unit = 1, Example: 1 | 2 represents 12
  0* | 1 1
  T | 2 2 2 3 3 3 3 3
  F | 4 4 4 4 4 4 5 5 5 5 5 5
  S | 6 6 6 6 7 7
  . | 8 8 9

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