Understanding Percentiles in Data

What is the formula to calculate the p-th percentile in grouped data?

• P = L - ((F - (N * (p/100))) / f) * c

• P = F + ((N * (p/100) + L) / c) * f

• P = L + ((N * (p/100) - F) / f) * c

• P = L + ((F * (p/100) - N) / f) * c

Given a frequency distribution, how do you determine the cumulative frequency?

• Cumulative frequency is calculated by subtracting each frequency from the total frequency.

• Cumulative frequency is determined by multiplying each frequency by its class midpoint.

• Cumulative frequency is the total of all frequencies divided by the number of classes.

• Cumulative frequency is calculated by adding each frequency to the sum of the previous frequencies.

If the 25th percentile of a dataset is 15, what does this indicate about the data?

• 75% of the data points are less than 15.

• 25% of the data points are less than or equal to 15.

• The median of the dataset is 15.

• 25% of the data points are greater than or equal to 15.

How do you find the percentile rank of a specific value in a grouped frequency table?

• Calculate the mean of the grouped data to find the percentile rank.

• Use the highest frequency value to determine the percentile rank.

• Add the values in the table and divide by the number of groups.

• Use the cumulative frequency and the total number of observations to calculate the percentile rank.

Calculate the 50th percentile (median) for the following data: 2, 4, 6, 8, 10, 12, 14, 16.

• 10

• 9

• 7

• 11

In a grouped frequency distribution, how do you handle classes with unequal widths when calculating percentiles?

• Use the midpoint of each class to calculate percentiles directly.

• Ignore the class widths and treat all classes as equal.

• Calculate percentiles based solely on the highest frequency class.

• Calculate cumulative frequencies and use relative frequencies to adjust for class widths.

If a dataset has 100 values, what position corresponds to the 90th percentile?

• 100

• 80

• 95

• 91

Explain how to interpret the 75th percentile in the context of a test score distribution.

• The 75th percentile is the score above which 75% of the scores fall.

• In a test score distribution, the 75th percentile is the score below which 75% of the scores fall.

• The 75th percentile indicates the highest score achieved in the test.

• The 75th percentile is the average score of all test takers.