Descriptive Statistics (Business Statistics)
Descriptive statistics turn raw business data into a clear picture. This chapter, from a business statistics course, covers displaying data with graphs, locating data with quartiles and percentiles, and measuring the centre with the arithmetic mean, median, mode, and the geometric mean used for average growth rates, along with skewness and measures of spread.
Displaying and Locating Data
A statistical graph helps reveal the shape of a data set and is often clearer than a mass of numbers. After displaying data, measures of location describe where particular values sit within it. Quartiles divide ordered data into four equal parts, and percentiles mark the value below which a given percentage of the data falls. In business these locate a figure against its peers, such as where a store’s sales rank among all branches.
Measures of the Centre
The centre of a data set can be summarised in several ways. The arithmetic mean, written with sigma notation, adds all values and divides by their count. The median is the middle value once data is ordered, and the mode is the most frequent value. This business-focused treatment also introduces the geometric mean, which multiplies the values and takes a root; it is the correct average for rates that compound, such as annual growth rates or investment returns, where the arithmetic mean would overstate the result.
Skewness and Spread
A distribution is symmetric when its values are balanced around the centre, and skewed when one tail is longer, which pulls the mean away from the median. Comparing the mean, median, and mode indicates the direction of skew. Spread is measured by the range, the difference between the largest and smallest values, and by the variance and its square root, the standard deviation, which describe how far values typically lie from the mean. Together these show both the shape and the variability of business data.
