Answer :
The median of MCAT scores is 25.7, and the first and third quartiles are 21.61 and 29.79, respectively.
The median of a normal distribution is equal to its mean, which in this case is 25.7. To find the first and third quartiles, we need to use the standard deviation.
The first quartile (Q1) is the score below which 25% of the data falls. To find Q1, we need to find the z-score that corresponds to the 25th percentile. Using a standard normal distribution table or calculator, we find that the z-score for the 25th percentile is -0.67.
We can then use the formula:
Q1 = mean + z * standard deviation
Q1 = 25.7 + (-0.67) * 6.5
Q1 = 21.61
The third quartile (Q3) is the score below which 75% of the data falls. To find Q3, we need to find the z-score that corresponds to the 75th percentile. Using a standard normal distribution table or calculator, we find that the z-score for the 75th percentile is 0.67.
We can then use the formula:
Q3 = mean + z * standard deviation
Q3 = 25.7 + (0.67) * 6.5
Q3 = 29.79
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