Given a data set with the mean = 44 and the standard deviation = 15, what is the value of the Third Quartile?
Third Quartile = 75th percentile
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the Z score = 75th percentile. Put the appropriate values into this equation to solve for the score.
Z = (score-mean)/SD
42
To find the value of the third quartile, we first need to understand what the third quartile represents. The third quartile, also known as the upper quartile, is the value below which 75% of the data falls.
To calculate the third quartile, we can use z-score and the standard normal distribution. The z-score formula is given by:
z = (X - μ) / σ
Where:
- X is the value we want to find the z-score for.
- μ is the mean of the dataset.
- σ is the standard deviation of the dataset.
To find the z-score corresponding to the third quartile, we use the fact that the third quartile corresponds to the 75th percentile. Using a standard normal distribution table or a calculator, we can find the z-score corresponding to the 75th percentile, which is approximately 0.6745.
Now, let's substitute the known values into the z-score formula:
0.6745 = (X - 44) / 15
Next, we solve for X by rearranging the equation:
X - 44 = 0.6745 * 15
X - 44 = 10.1175
X = 10.1175 + 44
X ≈ 54.1175
Therefore, the value of the third quartile is approximately 54.1175.