Quartiles-And-Percentiles gcse Edexcel

Quartiles

What are quartiles?

• The median splits the data set into two parts

  • Half the data is less than the median (and half the data is greater than it)

• Quartiles split the data set into four parts

  • The lower quartile (LQ) lies a quarter of the way along the data (when in order)

    • One quarter (25%) of the data is less than the LQ (and three quarters is greater than it)

  • The upper quartile (UQ) lies three quarters of the way along the data (when in order)

    • Three quarters (75%) of the data is less than the UQ (and one quarter is greater than it)

  • You may come across the median being referred to as the second quartile

How do I find the quartiles?

• There are two different methods for finding the quartiles

  • Use whichever method you find easiest

• In some cases the two methods will give slightly different answers

  • Either answer will receive full marks on the exam

  • Be sure to show your working so the examiner knows what you have done

Method 1

• Make sure the data is written in numerical order

• Use the median to divide the data set into lower and upper halves

  • If there are an even number of data values, then

    • the first half of those values are the lower half,

    • and the second half are the upper half

    • All of the data values are included in one or the other of the two halves

  • If there are an odd number of data values, then

    • all the values below the median are the lower half

    • and all the values above the median are the upper half

    • The median itself is not included as a part of either half

• The lower quartile is the median of the lower half of the data set

  • and the upper quartile is the median of the upper half of the data set

• Find the quartiles in the same way you would find the median for any other data set

  • just restrict your attention to the lower or upper half of the data accordingly

Method 2

• The quartiles can also be given in formula form:

  • For n data values

    • the lower quartile is the  value

    • the upper quartile is the  value

  • e.g. for 11 data values, <img alt=”fraction numerator 11 plus 1 over denominator 4 end fraction equals 3″ data-mathml=”<math ><semantics><mrow><mfrac><mrow><mn>11</mn><mo>+</mo><mn>1</mn></mrow><mn>4</mn></mfrac><mo>=</mo><mn>3</mn></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true,”toolbar”:”<toolbar ref=’general’><tab ref=’general’><removeItem ref=’setColor’/><removeItem ref=’bold’/><removeItem ref=’italic’/><removeItem ref=’autoItalic’/><removeItem ref=’setUnicode’/><removeItem ref=’mtext’ /><removeItem ref=’rtl’/><removeItem ref=’forceLigature’/><removeItem ref=’setFontFamily’ /><removeItem ref=’setFontSize’/></tab></toolbar>”}</annotation></semantics></math>” height=”47″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2247%22%20width%3D%2279%22%20wrs%3Abaseline%3D%2230%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E11%3C%2Fmn%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math12ed72e0d2d50af08c235c494fe’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADxjdnQgDVUNBwAAAVgAAAA6Z2x5ZoPi2VsAAAGUAAABK2hlYWQQC2qxAAACwAAAADZoaGVhCGsXSAAAAvgAAAAkaG10eE2rRkcAAAMcAAAADGxvY2EAHTwYAAADKAAAABBtYXhwBT0FPgAAAzgAAAAgbmFtZaBxlY4AAANYAAABn3Bvc3QB9wD6AAAE%2BAAAACBwcmVwa1uragAABRgAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACgAAAAGAAQAAQACACsAPf%2F%2FAAAAKwA9%2F%2F%2F%2F1v%2FFAAEAAAAAAAAAAAFUAywAgAEAAFYAKgJYAh4BDgEsAiwAWgGAAoAAoADUAIAAAAAAAAAAKwBVAIAAqwDVAQABKwAHAAAAAgBVAAADAAOrAAMABwAAMxEhESUhESFVAqv9qwIA%2FgADq%2FxVVQMAAAEAgABVAtUCqwALAEkBGLIMAQEUExCxAAP2sQEE9bAKPLEDBfWwCDyxBQT1sAY8sQ0D5gCxAAATELEBBuSxAQETELAFPLEDBOWxCwX1sAc8sQkE5TEwEyERMxEhFSERIxEhgAEAVQEA%2FwBV%2FwABqwEA%2FwBW%2FwABAAACAIAA6wLVAhUAAwAHAGUYAbAIELAG1LAGELAF1LAIELAB1LABELAA1LAGELAHPLAFELAEPLABELACPLAAELADPACwCBCwBtSwBhCwB9SwBxCwAdSwARCwAtSwBhCwBTywBxCwBDywARCwADywAhCwAzwxMBMhNSEdASE1gAJV%2FasCVQHAVdVVVQAAAQAAAAEAANV4zkFfDzz1AAMEAP%2F%2F%2F%2F%2FWOhNz%2F%2F%2F%2F%2F9Y6E3MAAP8gBIADqwAAAAoAAgABAAAAAAABAAAD6P9qAAAXcAAA%2F7YEgAABAAAAAAAAAAAAAAAAAAAAAwNSAFUDVgCAA1YAgAAAAAAAAAAoAAAAoQAAASsAAQAAAAMAXgAFAAAAAAACAIAEAAAAAAAEAADeAAAAAAAAABUBAgAAAAAAAAABABIAAAAAAAAAAAACAA4AEgAAAAAAAAADADAAIAAAAAAAAAAEABIAUAAAAAAAAAAFABYAYgAAAAAAAAAGAAkAeAAAAAAAAAAIABwAgQABAAAAAAABABIAAAABAAAAAAACAA4AEgABAAAAAAADADAAIAABAAAAAAAEABIAUAABAAAAAAAFABYAYgABAAAAAAAGAAkAeAABAAAAAAAIABwAgQADAAEECQABABIAAAADAAEECQACAA4AEgADAA