Charlotte received a score of 68 on both her English and Maths tests. The mean for English was 52 and the mean for Maths was 55. The standard deviations for English and Maths
were 10 and 8 respectively. In which subject did Charlotte perform better? Explain your decision.
please show working out
English
z = (68-52)/10 = 1.6 SDs above average
Math
z = (68 - 55)/8 = 1.625 SDs above average, better
Thats it Damon
its maths. Because std deviation is how far one is away from the mean.
To determine in which subject Charlotte performed better, we need to compare her scores in English and Maths to their respective means and standard deviations.
Step 1: Calculate the z-scores for Charlotte's scores in English and Maths using the formula:
z-score = (x - mean) / standard deviation
For English:
z-score for English = (68 - 52) / 10 = 16 / 10 = 1.6
For Maths:
z-score for Maths = (68 - 55) / 8 = 13 / 8 = 1.625
Step 2: Compare the z-scores for English and Maths.
The z-score represents how many standard deviations above or below the mean Charlotte's score was. In both subjects, Charlotte's z-score is positive, indicating that she scored above the mean.
Comparing the two z-scores, we see that Charlotte's z-score for Maths is higher (1.625) than her z-score for English (1.6). This means that her score in Maths is further above the mean compared to her score in English.
Conclusion:
Based on the z-scores, Charlotte performed better in Maths because her score was further above the mean compared to her score in English.