Rodney carried out an investigation to see whether two different mental health disorders influenced the ability to complete domestic tasks, such as being able to cook - AQA - A-Level Psychology - Question 3 - 2021 - Paper 2

First, we find the mean (average) of the domestic skills scores:

1. Calculate the sum of scores: $29 + 12 + 22 + 18 + 20 = 101$

2. Calculate the mean: $\text{Mean} = \frac{101}{5} = 20.2$

Next, we calculate the squared differences from the mean:

• For participant A: $(29 - 20.2)^2 = 76.84$
• For participant B: $(12 - 20.2)^2 = 67.24$
• For participant C: $(22 - 20.2)^2 = 3.24$
• For participant D: $(18 - 20.2)^2 = 4.84$
• For participant E: $(20 - 20.2)^2 = 0.04$

Sum of squared differences: $76.84 + 67.24 + 3.24 + 4.84 + 0.04 = 152.2$

To calculate the variance: $\text{Variance} = \frac{152.2}{5 - 1} = 38.05$

Finally, take the square root to find the standard deviation: $\text{Standard Deviation} = \sqrt{38.05} \approx 6.2$

Therefore, the standard deviation is approximately 6.2 when rounded to one decimal place.