Reporting Center and Spread | The Center for Quantitative Studies | Studio Aletheia
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Reporting Center and Spread

Lesson 13 · Application, Calculate Center and Spread

Data analysts calculate median, mode, range, and interquartile range every day to summarize real numbers for real decisions. Today you'll calculate all four for a workplace scenario and write the summary a manager would actually read.

Focus Reporting center and spread
Accountability Data Journal + Exit Ticket
Indicator Calculate the median, mode, range, and interquartile ...
The Center for Quantitative Studies Color Palette Aletheian Green · Aletheian Gold
Learning Targets

Learning Targets and Success Criteria

In the workplace, all four statistics work together to tell a complete, honest story.

Targets

What I will learn

  • I can calculate median, mode, range, and interquartile range for a real-world data set.
  • I can explain what each statistic reveals about a workplace decision.
  • I can write a short summary report using all four statistics.
  • I can recommend a decision based on center and spread evidence.
Success Criteria

What success looks like

  • I calculate all four statistics correctly for a real-world data set.
  • I explain the meaning of at least two statistics in plain language.
  • I write a clear summary report that uses all four statistics.
  • I make a recommendation supported by the calculated evidence.
Standard 6.DPSR.1.4

Calculate and report center and spread to support a real decision.

6.DPSR.1.4 — Calculate the median, mode, range, and interquartile range of a numerical data set.
Vocabulary

The words we'll use in today's lesson.

These terms will carry through today's mini-lesson, Data Lab, hands-on activity, journal, and exit challenge, and they'll keep coming back all year.

01 · Calculate

Median

The middle value of a data set when the values are ordered from least to greatest.

02 · Calculate

Mode

The value or values that occur most often in a data set.

03 · Calculate

Range

The difference between the greatest and least values in a data set.

04 · Calculate

Interquartile Range

The distance between the first quartile and the third quartile, showing the spread of the middle half of a data set.

College & Career Connections

Where this shows up in the real world.

Thinking like a mathematician is not just a school skill. It's what people get paid to do every day, in jobs you may not have heard of yet.

Data Analyst

Summarizing Weekly Sales for a Manager

A store manager wants to know how this week's sales went. A data analyst calculates the median sale amount, checks for a mode among common purchase sizes, finds the range from slowest to busiest day, and reports the interquartile range to show how consistent most days were, turning a week of numbers into four clear facts.

Data Scientist

Spotting Inconsistent Performance

A data scientist reviewing server response times calculates a small interquartile range alongside a large range and realizes most requests are fast and consistent, except for a few very slow outliers, exactly the kind of insight that tells an engineering team where to focus their fix.

Mini-Lesson

Four Statistics, One Report

In the workplace, all four statistics work together to tell a complete, honest story.

Imagine a manager asking: "How did we do this week?" A data analyst doesn't answer with just one number. They calculate the medianThe middle value of a data set when the values are ordered from least to greatest. sale amount to describe a typical sale, check the modeThe value or values that occur most often in a data set. to see if one purchase size is unusually common, find the rangeThe difference between the greatest and least values in a data set. to see the gap between the slowest and busiest day, and calculate the interquartile rangeThe distance between the first quartile and the third quartile, showing the spread of the middle half of a data set. to show how consistent the middle half of the days actually were.

Together, those four numbers answer questions no single statistic could answer alone: what's typical, what repeats often, how wide the extremes are, and how consistent the usual days are. That's exactly the kind of complete, evidence-based summary a real report needs before anyone makes a decision from it.

Adapted from Studio Aletheia's The Center for Quantitative Studies curriculum library, drawing on mathematical resources and the SC CCR Mathematics Standards.

Check for Understanding · CFU 1
This week's daily sales were 300, 350, 350, 400, 900 dollars. Calculate the median, mode, range, and interquartile range, then explain what they tell a manager about this week.
Toolkit

Materials for the Data Lab.

  • A. Workplace Data Set Cards
  • B. Summary Report Template
  • C. Ruler
  • D. Your Data Journal
  • E. A calculator (optional)
Non-negotiable routine

Order the data first, calculate all four statistics in order, then explain what each one means before writing any recommendation.

Guided Practice

Data Analyst Reporting Lab

You'll calculate all four statistics for a workplace data set and translate them into plain language.

Data Lab
Each scenario below is a real kind of data set an analyst might summarize for a manager's report.
1 · Order
Order your chosen workplace data set from least to greatest.
2 · Identify
Identify the median and mode of the data set.
3 · Describe
Describe the range and interquartile range, and what each reveals.
4 · Question
Write the recommendation question a manager would want answered from these statistics.
Hands-On

Write a Statistics Summary Report

You'll calculate all four statistics and write the report a data analyst would send to a manager.

1
Order: Order your chosen workplace data set from least to greatest.
2
Calculate: Calculate the median, mode, range, and interquartile range.
3
Translate: Translate at least two statistics into a plain-language sentence a manager would understand.
4
Recommend: Write a short recommendation based on the evidence from all four statistics.
Required

Data Journal Entry

Which Mathematical Process Standard did you rely on most today — Problem Solving, Connections, Representation & Communication, Analyze & Justify, or Structure & Patterns? Give one specific example from your Data Lab or hands-on work.
Checklist

Accountability Checklist

Required · Exit Challenge

Report the Full Picture

Server response times this week were 18, 20, 20, 24, 85 milliseconds. Calculate the median, mode, range, and interquartile range, then write one sentence a data analyst could use to summarize the week for an engineering team.

Lesson 13 · Application, Calculate Center and Spread

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