--- title: "Comparing data sets with averages and range" description: "Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers" canonical: https://lightmysky.com/learn/mathematics/comparing-data-sets-with-averages-and-range-mt_XSXnTQoQ4l source: https://lightmysky.com/learn/mathematics/comparing-data-sets-with-averages-and-range-mt_XSXnTQoQ4l.md retrieved: 2026-10-19 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Comparing data sets with averages and range Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers Subject: Mathematics · Area: Data & Statistics · Ages 11 to 13 Page: https://lightmysky.com/learn/mathematics/comparing-data-sets-with-averages-and-range-mt_XSXnTQoQ4l ## Ready when they can - Calculate mean, median, and mode for a data set and explain when each is most appropriate - Find the range of a data set and explain how an outlier affects the mean versus the median - Compare two data sets using their averages and ranges to draw conclusions ## Lesson: Comparing data sets with averages and range To find the mean, add the values and divide by how many there are, as you did with five pumpkins. One mean can hide differences between two data sets. The median is the middle value after ordering, or the mean of the two middle values when the count is even. The mode is the value that appears most often. The range measures spread: largest value minus smallest. **Example.** A team's ages are 12, 14, 12, 15, 12. Line them up in order: 12, 12, 12, 14, 15. The middle number is 12, so the median is 12. Since 12 shows up three times, more than any other age, the mode is also 12. *(drawing: Five kids picked blue, more than red or green, so blue is the mode of this group's favorite color.)* Outliers are values far from the rest. They can pull the mean up or down. The median uses the middle positions and is usually less affected by an extreme value. Adding or removing values can still change the median. When a data set has an outlier, the median often gives a better picture of a typical value. **Example.** Two pumpkin beds are weighed. Gate bed gives 3, 5, 6, 6 and 30 kg. Shed bed gives 8, 9, 9, 11 and 13 kg. Both add up to 50 kg, so both means are 10 kg. Put each set in order: Gate bed's median is 6 kg and Shed bed's is 9 kg. Their ranges also differ: 27 kg for Gate bed and 5 kg for Shed bed. To compare two sets, work out the same measure for both and say which measure you used. **Recap.** Median uses the middle value or pair; mode is most common; range is biggest minus smallest. Outliers can pull the mean up or down. Compare the same measures across sets. ## Practice 19 questions on this page, each with its working shown. ## Needs first - [Calculating the mean](https://lightmysky.com/learn/mathematics/calculating-the-mean-mt_Cg8VPguS_V) - [Frequency tables, bar charts and pie charts](https://lightmysky.com/learn/mathematics/frequency-tables-bar-charts-and-pie-charts-mt_eKJG-0eC6D) - [Statistical analysis vocabulary](https://lightmysky.com/learn/mathematics/statistical-analysis-vocabulary-mt_fmm-P17Vka) - [Line plots with fractions of a unit](https://lightmysky.com/learn/mathematics/line-plots-with-fractions-of-a-unit-mt_IHipFGTFEY) ## Opens up - [Averages from frequency tables](https://lightmysky.com/learn/mathematics/averages-from-frequency-tables-mt_5WF_Rhdb1X) - [Scatter Graphs & Correlation](https://lightmysky.com/learn/mathematics/scatter-graphs-and-correlation-mt_8atyuvPUZc) - [How a Chart Can Mislead](https://lightmysky.com/learn/mathematics/how-a-chart-can-mislead-mt_z7yMoRWipf)