Box Plots – GCSE Maths

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Introduction

  • Box plot is an important concept used in Statistics to represent quantities related to a given dataset graphically and helps us to provide conclusions about that dataset.
  • Box plots include graphical representation of these five quantities – Median, Maximum Value, Smallest value, First quartile and the Third Quartile.

Educational diagram showing the different box plots and how it is used in Statistics and in day to day life

Box Plots

  • Basically Box Plots are graphical representation of the following quantities which describe a dataset’s important features –
  • Example-image of a dataset of numbers arranged in a haphazard manner
  • Total values are 15 the increasing order of these will be –

series of numbers arranged in an ascending manner

  • Median – When the elements of the dataset are sorted( in increasing or decreasing order) then the middle element is called the Median.
  • Median will be the middle element that is 4, we can also use the following formula to find median –

Calculations showing how to calculate median from a given dataset for gcse maths

  • Greatest value – The maximum value among of dataset’s elements.
  • In the given example the greatest value is 9.
  • Smallest value – The smallest value among the elements.
  • In the given example the smallest value is 0.
  • Quartile(1st Quartile) – Basically it is first 25% part of the data. The formula to find 1st quartile is – Calculations showing how to calculate 1st quartile from a given dataset for plotting box plotsIn the given example-

Calculations showing how to calculate 1st quartile from a given dataset for plotting box plots

  • Quartile(3rd Quartile) – Basically it is first 75% part of the data. The formula to find 3rd quartile is –Calculations showing how to calculate 3rd quartile from a given dataset for plotting box plots

In the given example- Calculations showing how to calculate 3rd quartile from a given dataset for plotting box plotsBox plot for the given dataset showing smallest and greatest value, 1st and 3rd quartile and median for the given dataset

certified Physics and Maths tutorExamples including even and odd number of elements:

Problem: Draw the box plot for the following dataset –dataset for solved example for gcse maths containing minimum, maximum and median valuesSolution:GCSE Maths box plot showing minimum, maximum, quartiles, and median values for a given dataset.

certified Physics and Maths tutorExamples including even and odd number of elements:

Problem: Following is a dataset given that is the time taken by 11 students to complete an essay –dataset for a series of numbers for solved example for gcse maths(a) Write down the median time taken

(b) Find out the upper and lower Quartiles

(c) Draw the box plot for the dataset

Solution:

(a) Median for the dataset is- Calculation of median from the dataset(b) The upper and Lower Quartiles- Calculation of Lower quartile for box plots solved exampleUpper quartile (Q3) calculation for a dataset used to construct a GCSE Maths Box Plot(c) Box plot for the given dataset – Box plot for given data set for solved examples for gcse maths

certified Physics and Maths tutorExamples including even and odd number of elements:

Problem: Here is the data collected from a company of the experience of their 10 employees –data set for solved example of box plotsDraw the box plot for the data –images for solved examplesSolution:

To draw the box plot for the given dataset containing an even number of elements first we find Median, Quartiles and Minimum and Maximum value –calculations done for solved example to find median, 1st quartile and 3rd quartile for gcse maths

  • Final Answer- Completed GCSE Maths box plot showing minimum, Q1, median, Q3, and maximum values
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