IQR and Standard Deviation

The Interquartile Range (IQR) is a measure of statistical dispersion, representing the range between the first quartile (Q1) and the third quartile (Q3) in a data set. It is calculated as IQR = Q3 - Q1.

To calculate the IQR, first find Q1 (the median of the lower half of the data) and Q3 (the median of the upper half of the data). Then, subtract Q1 from Q3: IQR = Q3 - Q1.

A small IQR indicates that the data points are closely clustered around the median, suggesting low variability.

A large IQR indicates that the data points are spread out over a wider range, suggesting high variability.

The IQR is 3.

The formula for population standard deviation (σ) is: σ = √(Σ(xi - μ)² / N), where μ is the mean, xi are the data points, and N is the number of data points.

The standard deviation measures the amount of variation or dispersion of a set of values. A low standard deviation means that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.

The standard deviation is calculated based on the mean of the data set. It quantifies how much the individual data points deviate from the mean.

The 68-95-99.7 rule states that in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

The population standard deviation is 15.87.