The average, and when it lies to you

By the end of this lesson you can calculate the mean (the average) with a formula, and explain how one unusual value can pull it away from a typical day.

Why it matters

Amara buys fruit every morning. If she plans for an "average day" that is far too high, she buys fruit she cannot sell, and it goes bad. Averages appear in reports, news stories and school results all the time, so you need to know exactly what one does, and when it misleads.

The idea in plain words

Imagine Amara pours all the money from the week into one big bowl. Then she shares it out equally, so every day gets exactly the same amount. That equal share is the mean.

Mean (also called the average): add up all the values, then divide by how many values there are. Mean = total ÷ count.

There is a second way to picture it. Put every value on a seesaw, like coins at their spot on a long plank. The mean is the point where the plank balances.

The mean is the balancing point. One far-away value (the festival day) slides the balancing point a long way. Synthetic data.

Look at the bottom seesaw. Six days sit together on the left. One festival day sits far out on the right. To balance, the triangle has to move right, away from the six ordinary days.

See it done

Data: amara-stall-s1-takings.csv (synthetic). Rows 2 to 8 are days 1 to 7. Rows 16 to 22 are days 15 to 21.

Part A: an ordinary week (days 1 to 7).

1. Find the total: =SUM(D2:D8) gives ₦223,400.
2. Count the days: =COUNT(D2:D8) gives 7.
3. Share it out: ₦223,400 ÷ 7 = 31,914.2857... naira. The decimals never end.
4. Let the spreadsheet do it in one step: =AVERAGE(D2:D8) gives the same number. (Your sheet may show more or fewer decimal places.)
5. Money is easier to read in whole naira: =ROUND(AVERAGE(D2:D8), 0) gives ₦31,914.

The mean, ₦31,914, is close to the middle day from Lesson 1, ₦31,500. In an ordinary week, both tell a similar story.

Part B: the festival week (days 15 to 21).

1. =ROUND(AVERAGE(D16:D22), 0) gives ₦51,071.
2. Find the middle day the Lesson 1 way: =SMALL(D16:D22, 4) gives ₦32,400.
3. Count how many days were above the mean. COUNTIF counts the cells that pass a test. Here the test is ">"&AVERAGE(D16:D22), which means "greater than the average" (the & joins the > sign to the average). Type =COUNTIF(D16:D22, ">"&AVERAGE(D16:D22)). It gives only 1 of the 7 days. That day is the festival day, ₦155,300.

The festival week: the average line floats above six of the seven days. Synthetic data.

If Amara planned for ₦51,071 every day, she would overbuy on six days out of seven. The mean is not wrong: it is the true equal share. But here it does not describe a typical day.

Tip. In Excel the formulas are exactly the same: SUM, COUNT, AVERAGE and ROUND.

Your turn, with help

Amara's cousin Kofi runs another stall. His days 1 to 7 are in rows 32 to 38 of the same file. Find his mean, rounded to the nearest naira.

Hints: Use AVERAGE on D32:D38, wrapped in ROUND(..., 0). Then compare it with Amara's mean for her days 1 to 7.

Show the answer

=ROUND(AVERAGE(D32:D38), 0) gives ₦31,914. That is exactly the same as Amara's days 1 to 7! Both stalls took the same total in those seven days. Keep this in mind: it comes back at the end of the module.

Your turn, alone

1. Find Amara's mean for all 30 days (D2:D31), rounded to the nearest naira.
2. How many of the 30 days were above that mean? Use =COUNTIF(D2:D31, ">"&AVERAGE(D2:D31)).
3. Find the mean of the 30 days without the festival day (day 20 is in row 21): =ROUND(AVERAGE(D2:D20, D22:D31), 0). The comma lets AVERAGE take two ranges at once: rows 2 to 20, then rows 22 to 31. How much did one day change the mean?
4. Find Amara's mean for days 8 to 14 (D9:D15), rounded to the nearest naira.

Watch out

• Dividing by the wrong count. If one day is blank, the count is 6, not 7. AVERAGE skips empty cells and text, so check COUNT to see how many values it really used.
• Rounding too early. Round the final answer, not the numbers along the way, or small errors add up.
• Thinking the mean is a "typical" value. It is an equal share. One very big or very small value can drag it far from where most values sit. Always look at the values or a chart too.

Say it back

1. In words, how do you work out the mean?
2. Which spreadsheet formula gives the mean of D2:D8?
3. Six ordinary days and one huge day: is the mean nearer the six days, or pulled towards the huge day?

Show the answers

1. Add up all the values, then divide by how many values there are.
2. =AVERAGE(D2:D8).
3. Pulled towards the huge day, like the seesaw's balancing point.

What is next

One festival day pulled the mean far from a typical day, so Lesson 3 meets a centre that a single huge day cannot push around.

Formulas in this lesson were checked on 2026-10-09 against the official Google Sheets and Microsoft Excel help pages, and every number was calculated by running the formulas in a spreadsheet program (LibreOffice Calc) and checked by a separate calculation. Menu steps are written for Google Sheets on the web and Excel for Microsoft 365.

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Answers to Your turn, alone

Show the answers

1. =ROUND(AVERAGE(D2:D31), 0) gives ₦36,422.
2. 5 of the 30 days are above the mean. Most days are below it, because the festival day pulls the mean up.
3. Without the festival day the mean is ₦32,322. One day moved the mean from ₦32,322 to ₦36,422: up by about ₦4,099 (=AVERAGE(D2:D31) - AVERAGE(D2:D20, D22:D31), rounded).
4. =ROUND(AVERAGE(D9:D15), 0) gives ₦32,779.