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Standard Deviation, SM-Bank 010

A dataset is represented by the dot plot drawn below.
 

Determine the standard deviation of the dataset, giving your answer correct to two decimal places.   (2 marks)

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\(\text{Std Dev}\ = 1.25\)

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\(\text{Dataset values:}\ 0, 1, 1, 2, 2, 3, 4 \)

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

\(\text{Std Dev}\ = 1.245… = 1.25\ \text{(2 d.p.)} \)

Standard Deviation, SM-Bank 009

Isa Guha recorded the number of sixes hit in the first nine games of the Women's Big Bash Cricket League over two seasons.

The results are recorded in the two dot plots below.
  

  1. Determine the standard deviation of the results in Season 1, giving your answer correct to one decimal place.   (2 marks)

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

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i.    \(\text{Std Dev}\ = 1.9\ \text{(1 d.p.)} \)

ii.    \(\text{By inspection, season 1 has a slightly higher range}\)

\(\text{(5 vs 4) and its data points can be seen to be much}\)

\(\text{wider spread about the expected mean value.}\)

\(\text{Season 1 will therefore have a higher standard deviation.}\) 

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i.    \(\text{Season 1 dataset:}\ 6, 6, 7, 8, 10, 10, 10, 11, 11\)

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

\(\text{Std Dev}\ = 1.930… = 1.9\ \text{(1 d.p.)} \)
 

ii.    \(\text{By inspection, season 1 has a slightly higher range}\)

\(\text{(5 vs 4) and its data points can be seen to be much}\)

\(\text{wider spread about the expected mean value.}\)

\(\text{Season 1 will therefore have a higher standard deviation.}\) 

Standard Deviation, SM-Bank 004

Two data sets are represented in the dot plot diagrams below.
 

  1. Calculate the standard deviation of Data Set B, giving your answer correct to one decimal place.   (1 mark)

  2. Without using calculations, explain which data set has the highest standard deviation.  (2 marks)

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i.    \(\text{Std Dev}\ = 1.79… = 1.8\ \text{(1 d.p.)} \)

ii.   \(\text{By inspection, Data Set A has a smaller range and a tighter}\)

\(\text{spread against its expected mean value.}\)

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

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i.    \(\text{Data points:}\ 4, 4, 5, 5, 6, 6, 7, 8, 9, 9\)

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

\(\text{Std Dev}\ = 1.79... = 1.8\ \text{(1 d.p.)} \)
 

ii.   \(\text{By inspection, Data Set A has a smaller range and a tighter}\)

\(\text{spread against its expected mean value.}\)

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

Statistics, STD2 S3 2017 HSC 29d*

All the students in a class of 30 did a test.

The marks, out of 10, are shown in the dot plot.
 

  1. Find the median test mark.  (1 mark)

  2. The mean test mark is 5.4. The standard deviation of the test marks is 4.22.
  3. Using the dot plot, calculate the percentage of the marks which lie within one standard deviation of the mean.  (2 marks)
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  1. \(6\)
  2. \(\text{43%}\)
Show Worked Solution

i.    \(\text{30 data points}\)

\(\text{Median}\ = \dfrac{\text{15th + 16th}}{2} = \dfrac{4+8}{2} = 6\)
 

♦ Mean mark 50%.

ii.    \(\text{Lower limit}\ = 5.4-4.22 = 1.18\)

\(\text{Upper limit} = 5.4 + 4.22 = 9.62\)

\(\text{% between}\) \(= \dfrac{13}{30} \times 100\)  
  \(= 43.33… \%\)  
  \(=43\%\ \ \text{(nearest %)}\)  
♦♦ Mean mark 34%.