Percentiles and Z-Scores Flashcard Review

Front

What is a percentile?

Back

A percentile is a measure used in statistics to indicate the value below which a given percentage of observations in a group of observations falls.

Front

How do you calculate the percentile rank of a value?

Back

Percentile rank is calculated using the formula: \( P = \frac{(N_L + 0.5N_E)}{N} \times 100 \), where \( N_L \) is the number of values less than the score, \( N_E \) is the number of values equal to the score, and \( N \) is the total number of values.

Front

What is the 20th percentile?

Back

The 20th percentile is the value below which 20% of the data falls.

Front

What is a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean. It is calculated using the formula: \( z = \frac{(X - \mu)}{\sigma} \), where \( X \) is the value, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.

Front

How do you interpret a z-score of -1.02?

Back

A z-score of -1.02 means the value is 1.02 standard deviations below the mean.

Front

What does it mean if a height is in the 70th percentile?

Back

It means that the height is greater than 70% of the heights of people in the same age group.

Front

How do you find the 85th percentile in a data set?

Back

To find the 85th percentile, arrange the data in ascending order and use the formula: \( P_k = \frac{k}{100} \times (N + 1) \), where \( k \) is the desired percentile and \( N \) is the number of data points.

Front

What is the formula for calculating percentiles in a grouped frequency distribution?

Back

The formula is: \( P_k = L + \left( \frac{(k/100)N - CF}{f} \right) \times c \), where \( L \) is the lower boundary of the percentile class, \( CF \) is the cumulative frequency of the class before the percentile class, \( f \) is the frequency of the percentile class, and \( c \) is the class width.

Front

What is the significance of the mean in relation to z-scores?

Back

The mean is the central value around which z-scores are calculated; it serves as the reference point for determining how far a value is from the average.

Front

How do you interpret a percentile rank of 60?

Back

A percentile rank of 60 means that the value is higher than 60% of the data points in the distribution.