Unlock the power of statistics with our Enhanced Z-score Calculator. Quickly determine how far a data point is from the mean in terms of standard deviations.
A Z-score, also known as a standard score, indicates how many standard deviations an element is from the mean. It's a versatile tool used in statistics to compare data points from different normal distributions.
Understanding your Z-score is crucial for meaningful data analysis:
Use this calculator to gain insights into your data's distribution and identify significant values in your dataset.
A Z-score measures how many standard deviations away a data point is from the mean of a dataset. It helps in understanding the relative position of a value within a distribution.
Z = (x - μ) / σ
Where:
Given: A dataset of test scores with a mean (μ) of 75 and a standard deviation (σ) of 8. Calculate the Z-score for a student who scored 83.
Solution:
Applying the formula: Z = (83 - 75) / 8 = 8 / 8 = 1
Interpretation: The student's score is 1 standard deviation above the mean.
Given: The average height of plants in a garden is 30 cm with a standard deviation of 5 cm. Calculate the Z-score for a plant that is 22 cm tall.
Solution:
Applying the formula: Z = (22 - 30) / 5 = -8 / 5 = -1.6
Interpretation: The plant's height is 1.6 standard deviations below the mean.
Remember, Z-scores are particularly useful for comparing values from different normal distributions or for identifying outliers in a dataset.