5. Louise is interested to see whether there is a difference between the number of pictures recalled by children with dyslexia and by those who do not have dyslexia - AQA - A-Level Psychology - Question 5 - 2017 - Paper 1

To calculate the standard deviation:

1. Find the mean (average number of pictures recalled):

   ext{Mean} = rac{ ext{Sum of scores}}{ ext{Number of participants}} = rac{16 + 8 + 5 + 12 + 14 + 17 + 7 + 11 + 11 + 13}{10} = rac{ extbf{ 14}}{10} = 11.4

2. Calculate the variance:

   • Variance = rac{ ext{Sum of} (x_i - ext{mean})^2}{N} where $x_i$ is the score and $N$ is the number of scores.

   • Calculating $(x_i - ext{mean})^2$ for each:
     $(16 - 11.4)^2 = 21.16$
     $(8 - 11.4)^2 = 11.56$
     $(5 - 11.4)^2 = 40.96$
     $(12 - 11.4)^2 = 0.36$
     $(14 - 11.4)^2 = 6.76$
     $(17 - 11.4)^2 = 31.36$
     $(7 - 11.4)^2 = 19.36$
     $(11 - 11.4)^2 = 0.16$
     $(11 - 11.4)^2 = 0.16$
     $(13 - 11.4)^2 = 2.56$

   • Sum of squared differences = $21.16 + 11.56 + 40.96 + 0.36 + 6.76 + 31.36 + 19.36 + 0.16 + 0.16 + 2.56 = 133.4$

   • Variance = rac{133.4}{10} = 13.34

3. Find the standard deviation:

   • Standard Deviation = $ext{sqrt{variance}} = ext{sqrt{13.34}} \\$ = 3.65$ (rounded to two decimal places).

The standard deviation for the number of pictures recalled by children with dyslexia is 3.65.