# How to find percentile from z score?

The percentile is a statistical measure that indicates the value below which a given percentage of observations fall. In other words, it is a way to measure the relative standing of an individual in a group or population based on a particular attribute or characteristic. For example, if an individual’s height is at the 90th percentile, it means that 90% of the people in the group or population are shorter than them.

The z score, on the other hand, is a standard score that measures how many standard deviations an individual’s score is from the mean of a group or population. It is calculated by subtracting mean from the individual’s score and dividing the result by the standard deviation. The z score allows for comparing scores across different groups or populations, as it standardizes the scores by taking into account the mean and standard deviation of the group.

To find the percentile from a z score, it is necessary to use a z-score to percentile conversion table or a z-score to percentile calculator. This process involves converting the z score to a probability using a standard normal distribution table or calculator and then using this probability to find the corresponding percentile. Here, we will explain the steps involved in finding the percentile from a z score using a z-score to the percentile conversion table.

## How to find percentile from z score?

### Step 1: Determine the z score

The first step in finding the percentile from a z score is to determine the z score of the individual. As mentioned above, the z score is calculated by subtracting the mean from the individual’s score and dividing the result by the standard deviation. For example, if the mean score of a group is 50 and the standard deviation is 10, and an individual’s score is 75, their z score would be calculated as follows:

Z score = (Individual’s score – Mean score) / Standard deviation

= (75 – 50) / 10

= 2.5

### Step 2: Convert the z score to a probability

The next step is to convert the z score to a probability. This is done using a standard normal distribution table or calculator, which gives the probability of obtaining a score equal to or less than the given z score.

To use a standard normal distribution table, locate the row corresponding to the first digit of the z score (in this case, 2) and the column corresponding to the second digit of the z score (in this case, 5). The probability listed in the table at the intersection of these two values is the probability of obtaining a score equal to or less than the given z score.

For example, using a standard normal distribution table, the probability of obtaining a score equal to or less than 2.5 is 0.9938.

To use a standard normal distribution calculator, input the z score, and the calculator will give the corresponding probability.

### Step 3: Find the percentile using the probability

The final step is to use the probability obtained in Step 2 to find the corresponding percentile. This can be done using a percentile conversion table or a percentile calculator.

To use a percentile conversion table, locate the row corresponding to the percentile (in this case, 99) and the column corresponding to the probability (in this case, 0.9938). The value listed in the table at the intersection of these two values is the corresponding percentile.

For example, using a percentile conversion table, the percentile corresponding to a probability of 0.9938 is 99.38.

To use a percentile calculator, input the probability, and the calculator will give the corresponding percentile.

## Conclusion:

In conclusion, finding the percentile from a z score can be accomplished using the standard normal distribution table or online calculators. To use the table, first, locate the z score in the left column and then find the corresponding percentile in the right column. If the z score falls between two values in the table, then the percentile can be estimated by interpolating between the two percentiles. Alternatively, online calculators can be used to find the percentile directly from the z score. It is important to note that the percentile represents the proportion of values in a distribution that is equal to or below the value corresponding to the z score. Therefore, finding the percentile from a z score can provide valuable information about how an individual score compares to the rest of the population.