2. Measures of Dispersion

Understanding Variance, Standard Deviation, and Z-Scores

• Range is calculated by subtracting the minimum value from the maximum value in a dataset and reflects the degree of variance and spread from the mean.
• A small range indicates less deviation from the mean, making the mean a good indication of future values, while a large range suggests a greater chance that future values will not be close to the mean.
• Standard deviation is a more precise measure of dispersion compared to range, providing a specific range of values that captures a specific percentage of the dataset.
• Standard deviation breaks the dataset into standardized blocks based on percent difference from the mean and can be used to determine the percentage of values within certain ranges from the mean.
• The formula for standard deviation in Excel and Google Sheets is =STDEV(A1:A2), providing the standard deviation for values in the range of cells.
• Standard deviation can be used to determine variance based on a normal distribution curve, estimating that about 95% of the data should fall within the range of two standard deviations from the mean.
• Three standard deviations are likely to capture 99% of the typical data, suggesting that any values outside this range would represent statistical outliers.
• Z-scores indicate how far a value is from the mean in terms of standard deviations and provide a way to compare a specific value to the observed distribution of values within a dataset.
• The z-score of a value tells how many standard deviations away from the mean that value lies, providing a precise indication of its position within the dataset.
• A z-score of -2.6 for an age of 37 indicates that the age lies 2.6 standard deviations below the mean, making it atypical for the population.
• A z-score table can be used to find the percentage of values associated with a specific z-score, showing how atypical a value is within the dataset.
• For example, a z-score of -2.6 for age 37 indicates that the age is further from the mean than 99.53% of the typical customer population, making it a statistical outlier.

Understanding Variance, Standard Deviation, and Z-Scores

• Range is calculated by subtracting the minimum value from the maximum value in a dataset and reflects the degree of variance and spread from the mean.
• A small range indicates less deviation from the mean, making the mean a good indication of future values, while a large range suggests a greater chance that future values will not be close to the mean.
• Standard deviation is a more precise measure of dispersion compared to range, providing a specific range of values that captures a specific percentage of the dataset.
• Standard deviation breaks the dataset into standardized blocks based on percent difference from the mean and can be used to determine the percentage of values within certain ranges from the mean.
• The formula for standard deviation in Excel and Google Sheets is =STDEV(A1:A2), providing the standard deviation for values in the range of cells.
• Standard deviation can be used to determine variance based on a normal distribution curve, estimating that about 95% of the data should fall within the range of two standard deviations from the mean.
• Three standard deviations are likely to capture 99% of the typical data, suggesting that any values outside this range would represent statistical outliers.
• Z-scores indicate how far a value is from the mean in terms of standard deviations and provide a way to compare a specific value to the observed distribution of values within a dataset.
• The z-score of a value tells how many standard deviations away from the mean that value lies, providing a precise indication of its position within the dataset.
• A z-score of -2.6 for an age of 37 indicates that the age lies 2.6 standard deviations below the mean, making it atypical for the population.
• A z-score table can be used to find the percentage of values associated with a specific z-score, showing how atypical a value is within the dataset.
• For example, a z-score of -2.6 for age 37 indicates that the age is further from the mean than 99.53% of the typical customer population, making it a statistical outlier.

Test your knowledge of variance, standard deviation, and z-scores with this quiz. Explore concepts such as range, standard deviation, and how z-scores indicate the position of a value within a dataset. Perfect for anyone looking to strengthen their understanding of statistical measures and their practical applications.