Mathematics

 

Data Handling: Cumulative Frequency, Quartiles and IQR

Cumulative Frequency

The marks obtained by a group of students for maths are as follows:

Marks (x)frequency (f)
0 - 203
21 - 406
41 - 609
61 - 808
81 - 1004

Now, we can rearrange the table with a running-total as frequency. This frequency is called cumulative frequency. A cumulative frequency table consists of classes up to a certain upper value and cumulative frequencies, which takes the following form.


Marks (x)cumulative frequency (f)
up to 203
up to 409
up to 6018
up to 8026
up to 10030

Now you can plot a graph to represent the above data and it looks like the following:

 

graph

 

From the graph, we can find the the following:

Now, we can draw a box plot; it shows the minimum-value, LQ, Median, UQ and maximum value in that order as shown in the image.

Practise Box Plots - interactive

A box-plot shows the minimum value, Q1, median, Q3 and the maximum value in that order.

With the following applet, you can see how a box plot is created with a set of data. Just click the button to get a new set of data and see how the box-plot is formed. You may have to move the grid to see the full box-plot.

Averages and Spread of Data with Excel

In the following animation, a set of random data is generated with Excel and then averages and spread of data are calculated - automatically.

statistics with excel

 

Practise Cumulative Frequency - interactive

With the following applet, you can practise cumulative frequency interactively. With each click, a new dataset is created and the cumulative frequency curve is updated accordingly. You can see the quartiles and the median being updated too. The set of data gives the marks obtained by a group of students in a certain test.

 

Now, in order to complement what you have learnt so far, work out the following:

  1. The time taken for a certain test by a group of students are is as follows:
    Marks (x) frequency (f)
    11 - 203
    21 - 307
    31 - 4018
    41 - 505
    51 - 602

    Find the following:

    1. the median
    2. quartiles
    3. IQR
    4. the pass mark, if 4/7th of the students are passed
    5. the number of students who scored more than 50
  2. The time taken by 25 kids to finish their lunch, in minutes, is as follows:
    8, 9, 7, 11, 7, 12, 15, 9, 9, 10, 11, 17, 16, 10, 11, 6, 19, 12, 17, 15, 16, 12, 13, 13, 17
    Construct an appropriate grouped-frequency table for this data and then plot a cumulative frequency graph for the same. Then calculate the mean, median, quartiles and IQR for the data.

 

 

Human Anatomy in a Cube - highly recommended

If you want to learn the important facts about human anatomy in a short period time - with fun - here is an amazing invention. It's an interactive cube with with clear labels; you can learn many systems in a matter of seconds. It's unique, elegant and above all, first of its kind.

The Solar System in a Cube - highly recommended

If you want to learn the important facts about our solar system, especially the planets, in a short period time - with fun - here is an amazing invention. It's an interactive cube with with important facts in a nut-shell; you can learn a lot in a matter of seconds. It's unique, elegant and above all, first of its kind.

This is how these cubes work:

 

Now that you have read this tutorial, you will find the following tutorials very helpful too:

 

 

Recommended Reading


 

Maths is challenging; so is finding the right book. K A Stroud, in this book, cleverly managed to make all the major topics crystal clear with plenty of examples; popularity of the book speak for itself - 7th edition in print.

Recommended - GCSE & iGCSE


 

This is the best book available for the new GCSE(9-1) specification and iGCSE: there are plenty of worked examples; a really good collection of problems for practising; every single topic is adequately covered; the topics are organized in a logical order.

Recommended for A Level


 

This is the best book that can be recommended for the new A Level - Edexcel board: it covers every single topic in detail;lots of worked examples; ample problems for practising; beautifully and clearly presented.