STATISTICAL QUALITY CONTROL

What is Central Tendency?

Central tendency refers to the statistical measure that identifies a single score as representative of an entire distribution.

Mean

The mean is the average of a set of numbers, calculated by summing all values and dividing by the count.

Median

The median is the middle value in a dataset when the numbers are arranged in order. If even, it is the average of the two middle values.

Mode

The mode is the value that appears most frequently in a dataset.

Characteristics of Mean

The mean is sensitive to extreme values (outliers), which can skew the result.

Characteristics of Median

The median is robust against outliers and provides a better measure of central tendency for skewed distributions.

Characteristics of Mode

The mode can be used with nominal data and may have multiple values or none at all.

When to use Mean

Use the mean when data is symmetrically distributed without outliers.

When to use Median

Use the median for skewed distributions or when outliers are present.

When to use Mode

Use the mode in categorical data to find the most common category.

What are Measures of Spread?

Measures of spread describe the variability or dispersion within a dataset, indicating how much the data points differ from the central tendency.

Range

The range is the difference between the highest and lowest values in a dataset.

Variance

Variance measures the average of the squared differences from the mean, indicating how spread out the data points are.

Standard Deviation

Standard deviation is the square root of the variance, providing a measure of spread in the same units as the data.

Interquartile Range (IQR)

The IQR is the difference between the first quartile (Q1) and the third quartile (Q3), representing the middle 50% of the data.

Coefficient of Variation

The coefficient of variation is the ratio of the standard deviation to the mean, expressed as a percentage, used to compare relative variability.

Outliers

Outliers are data points that significantly differ from the other observations in the dataset, which can affect measures of spread.

Box Plot

A box plot visualizes the distribution of data based on a five-number summary: minimum, Q1, median, Q3, and maximum.

What does a high variance indicate?

A high variance indicates that data points are spread out over a wide range of values.

What does a low standard deviation indicate?

A low standard deviation indicates that data points tend to be close to the mean of the dataset.