Concept · C:arithmetic-mean

Arithmetic mean

Working definition

A measure of center equal to the sum of quantitative observations divided by their count, with every observation contributing to the result.

Also calledMean · Average

Add the observations and divide by their count. For Juniper Year 1:

[ \bar{x}=\frac{510}{16}=31.875\text{ days}. ]

The unit remains days. The bar marks this as a sample mean; it is not the unknown mean for all 480 qualifying invoices.

Every value moves the mean

The mean is the point at which signed deviations sum to zero. That property makes it central to variance, standard error, and many estimation methods. It also makes the mean responsive to tails. Juniper Year 2's 78-day invoice raises its mean above its median. Deleting the invoice would lower the mean, but a numerical effect is not a reason to delete valid data.

Average of what, weighted how?

One row receives one unit of weight in this arithmetic mean. If rows represent invoice lines rather than invoices, or if the decision needs dollars weighted by invoice amount, the estimand changes. A mean of entity returns also differs from a value-weighted portfolio return. State the unit and weighting rule.

Use the mean with an ordered-value or graphical view and a spread measure. A smaller mean settlement time is a sample observation, not proof of improved collections, lower credit risk, or future cash performance.

Arithmetic mean is shown with up to six authored relationships selected from the validated learning graph.
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Learning objectives

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Learning level

Understand this concept

  • Explain the arithmetic mean as a balance-point summary that uses every quantitative value and is therefore sensitive to extreme observations.
Learning level

Apply this concept

  • Compute and compare sample or population means from declared quantitative series while preserving units, denominator, scope, and outlier treatment.

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Use this idea next

  • Arithmetic mean — Apply

    Required level here: understand. Required. Calculation applies the sum-and-count definition and its interpretation.

  • Variance — Understand

    Required level here: apply. Required. Variance measures squared distance from the correctly computed mean.

Updated Aug 7, 2026 Review due Nov 7, 2026