Mode-And-Mean-From-Grouped-Data gcse Edexcel

Mode & Mean from Grouped Data

How do I estimate the mean for grouped data?

• It is impossible to find the mean for grouped data, because we don’t have access to the original data values

  • i.e. there is no way to find the exact sum of all the data values

  • so we can’t use the formula

• However we can estimate the mean for grouped data

  • To do this we use the class midpoints as our data values

    • e.g. if a class interval is 150 ≤ x < 160

    • we assume that all the data values are equal to the midpoint, 155

• STEP 1
  Draw an extra two columns on the end of a table of the grouped data

  • In the first new column write down the midpoint of each class interval

  • If the midpoint isn’t obvious, add the endpoints and divide by 2

    • e.g. if a class interval is 150 ≤ x < 160

    • the midpoint is

• STEP 2
  Calculate “frequency” × “midpoint” (this is often called fx)

  • Write these values in the second column you added to the table

• STEP 3
  Total the fx column and (if necessary) the frequency column

  • The question may already tell you the total number of data values (i.e. the total frequency)

    • In that case there’s no need to find the total of the frequency column

• STEP 4
  Estimate the mean by using the formula

  • 

    • i.e. divide the total of the fx column by the total number of data values

How do I find the modal class?

• It is impossible to find the modal value (i.e. mode) for grouped data, because we don’t have access to the original data values

  • i.e. it is impossible to say which value occurs the most times

• For grouped data we talk about the modal class instead

  • This is the class with the highest frequency

    • Just find the highest frequency in the table

    • The corresponding class interval tells you the modal class

• Be careful not to confuse the modal class with its frequency

  • e.g. if the highest frequency in the table is 34, corresponding to the class interval <img alt=”40 less or equal than x less than 50″ data-mathml=”<math ><semantics><mrow><mn>40</mn><mo>&#8804;</mo><mi>x</mi><mo>&#60;</mo><mn>50</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=”22″ 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%2222%22%20width%3D%2279%22%20wrs%3Abaseline%3D%2216%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E40%3C%2Fmn%3E%3Cmo%3E%26%23×2264%3B%3C%2Fmo%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmn%3E50%3C%2Fmn%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math1d3114856d6c6df443e3168d768’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADxjdnQgDVUNBwAAAVgAAAA6Z2x5ZoPi2VsAAAGUAAABNWhlYWQQC2qxAAACzAAAADZoaGVhCGsXSAAAAwQAAAAkaG10eE2rRkcAAAMoAAAADGxvY2EAHTwYAAADNAAAABBtYXhwBT0FPgAAA0QAAAAgbmFtZaBxlY4AAANkAAABn3Bvc3QB9wD6AAAFBAAAACBwcmVwa1uragAABSQAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACgAAAAGAAQAAQACADwiZP%2F%2FAAAAPCJk%2F%2F%2F%2Fxd2eAAEAAAAAAAAAAAFUAywAgAEAAFYAKgJYAh4BDgEsAiwAWgGAAoAAoADUAIAAAAAAAAAAKwBVAIAAqwDVAQABKwAHAAAAAgBVAAADAAOrAAMABwAAMxEhESUhESFVAqv9qwIA%2FgADq%2FxVVQMAAAIAgABVAoACqwAFAAsAbBiwQRoAsQAAExCxAAbksQABExCwCTyxAQX1sAo8sAAQsQUD9bECBe2xBAP1sQMF7bAKELELA%2FWxCAXtsQYD9bEHBe0BsAwQsQED9rIJAAo8PDyxBQT1sgIICzw8PLEEBPWyBgcDPDw8sQ0D5hMHBRc1JwE1DQEXN4EBAQD%2F%2FwEA%2FwD%2FAAH%2FAatWgIBWgAEqVoCAVoAAAwCA%2F6sCgAKrAAMABwALAC8YAQCxCQA%2FsQgF5LECBfSxAQT0sQYF9LEDBOSxBQT0sQQF9LEHARA8sQAGEDwwMRMHATUTNQEXATUhFYEBAf8B%2FgABAf%2F%2BAAGrVv8AVgGqVv8AVv5WVVUAAAAAAQAAAAEAANV4zkFfDzz1AAMEAP%2F%2F%2F%2F%2FWOhNz%2F%2F%2F%2F%2F9Y6E3MAAP8gBIADqwAAAAoAAgABAAAAAAABAAAD6P9qAAAXcAAA%2F7YEgAABAAAAAAAAAAAAAAAAAAAAAwNSA