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Standard Deviation, SM-Bank 011

Mr Ralph has a History class that has completed two separate exams during the term.

The results of each exam are summarised in the histograms below.
 

Without using calculations, explain which test will have the highest standard deviation.  (2 marks)

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\(\text{By inspection, Test B has a higher range than Test A.}\)

\(\text{Test A results look to have a tighter spread of data points}\)

\(\text{about its expected mean, when compared to Test B.}\)

\(\text{Test B will therefore have a higher standard deviation.}\) 

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\(\text{By inspection, Test B has a higher range than Test A.}\)

\(\text{Test A results look to have a tighter spread of data points}\)

\(\text{about its expected mean, when compared to Test B.}\)

\(\text{Test B will therefore have a higher standard deviation.}\) 

Standard Deviation, SM-Bank 012

Seven 40-year old males are asked how many children they have in a survey.

The results are summarised in the histogram drawn below.
 

  1. Determine the mean number of children of the group surveyed, giving your answer to two decimal places.   (1 mark)

  2. Calculate the standard deviation of this data set, giving your answer to two decimal places.   (1 mark)

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i.    \(\text{Mean}\ = 2.57\)

ii.   \(\text{Std Dev}\ = 1.05\)

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i.    \(\text{Dataset values:}\ 1, 2, 2, 2, 3, 4, 4 \)

\(\text{Mean}\ = \dfrac{1+2+2+2+3+4+4}{7} = \dfrac{18}{7} = 2.571… = 2.57\ \text{(2 d.p.)} \)
 

ii.    \(\text{By calculator (using Statistics mode):} \)

\(\text{Std Dev}\ = 1.049… = 1.05\ \text{(2 d.p.)} \)