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. The children have been given a short recall task to see how many of the pictures they can remember out of 20. Table 2 shows the raw data from the experiment. Table 2 Participant number Number of pictures recalled by children with dyslexia Number of pictures recalled by children without dyslexia 1 16 11 2 8 9 3 5 7 4 12 17 5 14 4 6 17 9 7 11 11 8 11 6 9 13 12 10 Range Table 2 (a) Calculate the range of scores Louise gathered in both conditions of her study and complete Table 2 above. (b) Calculate the standard deviation for the number of pictures recalled by children with dyslexia. Show your working and give your answer to two decimal places.

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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

Question 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. Th... show full transcript

Worked Solution & Example Answer: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

Step 1

Calculate the range of scores Louise gathered in both conditions of her study and complete Table 2 above.

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Answer

To calculate the range for the numbers recalled by children with dyslexia, we first identify the maximum and minimum values.

Maximum recalled: 17
Minimum recalled: 5

The range is calculated as:

$\text{Range} = \text{Maximum} - \text{Minimum} = 17 - 5 = 12$

For children without dyslexia:

Maximum recalled: 17
Minimum recalled: 4

The range is:

$\text{Range} = 17 - 4 = 13$

Thus, the completed table should display:

For dyslexia: Range = 12
For non-dyslexia: Range = 13.

Step 2

Calculate the standard deviation for the number of pictures recalled by children with dyslexia. Show your working and give your answer to two decimal places.

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Answer

To find the standard deviation, we use the formula:

$\sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{n}}$

Where:

$\sigma$ = standard deviation
$x_i$ = each value
$\mu$ = mean of the values
$n$ = number of values

First, calculate the mean ( $\mu$ ) of the scores recalled by children with dyslexia:

Scores: 16, 8, 5, 12, 14, 17, 11, 11, 13
Total = 16 + 8 + 5 + 12 + 14 + 17 + 11 + 11 + 13 = 107
Mean = $\mu = \frac{107}{9} \approx 11.89$

Next, calculate the squared differences from the mean:

For 16: $(16 - 11.89)^2 = 17.47$
For 8: $(8 - 11.89)^2 = 15.29$
For 5: $(5 - 11.89)^2 = 47.72$
For 12: $(12 - 11.89)^2 = 0.0121$
For 14: $(14 - 11.89)^2 = 4.46$
For 17: $(17 - 11.89)^2 = 26.57$
For 11: $(11 - 11.89)^2 = 0.7921$
For 11: $(11 - 11.89)^2 = 0.7921$
For 13: $(13 - 11.89)^2 = 1.24

Sum of squared differences = 17.47 + 15.29 + 47.72 + 0.0121 + 4.46 + 26.57 + 0.7921 + 0.7921 + 1.24 = 113.6221
Divide by n (number of scores = 9):

$\frac{113.6221}{9} \approx 12.69$

Finally, take the square root:

$\sigma \approx \sqrt{12.69} \approx 3.56$

Thus, the standard deviation is approximately 3.56.

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

Worked Solution & Example Answer: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

Calculate the range of scores Louise gathered in both conditions of her study and complete Table 2 above.

Calculate the standard deviation for the number of pictures recalled by children with dyslexia. Show your working and give your answer to two decimal places.

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