### Standard Deviation and standard deviation after data changing

Question Sample Titled 'Standard Deviation and standard deviation after data changing'

The standard deviation of the project scores obtained by a group of students in a Liberal Education project is ${11}$ $\text{marks}$. The teacher thinks the scores are too low, so she adjusts the project score of each student such that each score is increased by ${20}\%$ and extra ${9}$ $\text{marks}$ are added.

 (a) Find the standard deviation of the project scores after the score adjustment. (1 mark) (b) Is there any change in the standard score of each student due to the score adjustment? Explain your answer. (2 marks)

 (a) The standard deviation  $={11}{\left({1}+{20}\%\right)}$  $={13.2}$ $\text{marks}$ 1A (b) Let ${x}$ be the project score and $\overline{{x}}$ be the mean of the project scores before the adjustment. The standard score before the score adjustment.   $=\dfrac{{{x}-\overline{{x}}}}{{11}}$ The standard score after the score adjustment  $=\dfrac{{{\left({x}{\left({1}+{20}\%\right)}+{9}\right)}-{\left(\overline{{x}}{\left({1}+{20}\%\right)}+{9}\right)}}}{{13.2}}$ 1M  $=\dfrac{{{1.2}{\left({x}-\overline{{x}}\right)}}}{{13.2}}$  $=\dfrac{{{x}-\overline{{x}}}}{{11}}$ Thus, there is no change in the standard score of each student due to the score adjustment. 1A f.t.

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