Other-Types-Of-Mean gcse Edexcel

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Exam code:1ST0

Weighted Mean

What is a weighted mean?

A weighted mean is used when different numbers or values have different weights
- i.e. some of the values have more statistical ‘importance’ than others
To find the weighted mean from a list of values and weights
- $weighted space mean equals fraction numerator sum for blank of open parentheses value cross times weight close parentheses over denominator sum for blank of weights end fraction$
  - $sum for blank of open parentheses value cross times weight close parentheses$ means multiply each value by its weight and add all the products together
  - $sum for blank of weights$ means add all the weights together
- This formula is not on the exam formula sheet, so you need to remember it
An exam question may tell you what weights to use
- e.g. three test papers where Paper 1 has a weight of 25, Paper 2 has a weight of 35, and Paper 3 has a weight of 40
But often the weights need to be determined from context
- The weights could be the percentages of individuals to which different values apply
- If you know the means for separate groups, the overall mean is a weighted average
  - In this case the numbers of individuals in each group are the weights
- See the Worked Example

Examiner Tips and Tricks

If the values and weights are given to you in a table
- add an extra column for working out ‘value × weight’
You may need to consider the context of a question to decide whether a weighted average is necessary

Worked Example

(a) Myfanwy sits three test papers. Paper 1 has a weight of 25, Paper 2 has a weight of 35, and Paper 3 has a weight of 40. She scores 64% on Paper 1, 60% on Paper 2, and 75% on Paper 3. Work out Myfanwy’s final mark.

Use the weighted average formula <img alt=”weighted space mean equals fraction numerator sum for blank of open parentheses value cross times weight close parentheses over denominator sum for blank of weights end fraction” data-mathml=”<math ><semantics><mrow><mi>weighted</mi><mo> </mo><mi>mean</mi><mo>=</mo><mfrac><mrow><munder><mo>∑</mo><mrow/></munder><mfenced><mrow><mi>value</mi><mo>×</mo><mi>weight</mi></mrow></mfenced></mrow><mrow><munder><mo>∑</mo><mrow/></munder><mi>weights</mi></mrow></mfrac></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>” data-type=”commentary” height=”71″ 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%2271%22%20width%3D%22279%22%20wrs%3Abaseline%3D%2242%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Eweighted%3C%2Fmi%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmi%3Emean%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmunder%3E%3Cmo%3E%26%23×2211%3B%3C%2Fmo%3E%3Cmrow%2F%3E%3C%2Fmunder%3E%3Cmfenced%3E%3Cmrow%3E%3Cmi%3Evalue%3C%2Fmi%3E%3Cmo%3E%26%23xD7%3B%3C%2Fmo%3E%3Cmi%3Eweight%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmunder%3E%3Cmo%3E%26%23×2211%3B%3C%2Fmo%3E%3Cmrow%2F%3E%3C%2Fmunder%3E%3Cmi%3Eweights%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math14d934f2e8abd0f03b4aad4c26a’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAAERjdnQgDVUNBwAAAWAAAAA6Z2x5ZoPi2VsAAAGcAAABqmhlYWQQC2qxAAADSAAAADZoa

Statistics Gcse Edexcel Higher

Other-Types-Of-Mean gcse Edexcel

Weighted Mean

What is a weighted mean?

Examiner Tips and Tricks

Worked Example

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