A teacher wants to assign an 'A' grade to everyone that scores in the 80th percentile. The grades are: 8 10 12 15 25 40 50 55 60 75 85 90 What is the 80th percentile value What is the meaning
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A teacher wants to assign an 'A' grade to everyone that scores in the 80th percentile. The grades are: 8 10 12 15 25 40 50 55 60 75 85 90
- What is the 80th percentile value
- What is the meaning
The 80th percentile value is 75 and it is calculated below:
From the given information, the grades are 8, 10, 12, 15, 25, 40, 50, 55, 60, 75, 85 and 90.
That is, there are 12 scores. Hence, the sample size is n=12.
Step 1: Arrange the scores in ascending order.
8, 10, 12, 15, 25, 40, 50, 55, 60, 75, 85 and 90.
Step 2: Find the value of sample size*percentile.
12*80th percentile=12*0.80=9.6.
Step 3: Here, the value 9.6 is fractional value. Hence, round the value to nearest integer.
That is, the nearest integer value is 10.
Step 4: The value of 80th percentile lies at the 10th position in the ascending ordered scores.
The value at 10th position is 75.
Step 5: The 80th percentile value is 75.
Step by step
Solved in 2 steps
