A pile of numbers has a middle

By the end of this lesson you can put a small set of numbers in order and find the middle one, by hand and with a spreadsheet formula.

Why it matters

Amara sells fruit in Lagos. She hands you a week of daily takings and asks: "Was this a normal week?" Seven numbers are hard to hold in your head. One number that stands for the whole week is easy to remember, compare and plan with.

The idea in plain words

Picture seven children lining up for a photo, shortest on the left, tallest on the right. Who stands in the middle? The fourth child: three are shorter, three are taller. That child tells you roughly how tall "a typical child" in the group is.

Numbers work the same way. Line them up from smallest to largest, then look at the one in the middle.

Sorting the week: once the cards are in order, the middle card is easy to spot. Synthetic data.

Sort: put values in order, here from smallest to largest.

Centre: a single value that sits in the middle of a pile of numbers and stands for a "typical" one. This module meets three kinds of centre.

How do you find the middle position? If you have an odd number of values (like 7), add 1 and halve it:

(7 + 1) ÷ 2 = 4, so the middle is the 4th value in order.

See it done

Data: amara-stall-s1-takings.csv. Synthetic data: a computer made up these numbers. Column D, takings_ngn, is the money taken each day, in naira (₦). Rows 2 to 8 are Amara's days 1 to 7 (Monday to Sunday).

Formula: an instruction you type into a cell, starting with =, that tells the spreadsheet to work something out. Range: a block of cells, written as first cell, colon, last cell. D2:D8 means cells D2, D3, D4, D5, D6, D7 and D8.

1. Open the file. In Google Sheets choose File, then Import, then Upload, and pick amara-stall-s1-takings.csv. Choose Create new spreadsheet, then click Import. In Excel, open the file with File, then Open.
2. Read the week in day order. Cells D2 to D8 hold: ₦30,600, ₦33,600, ₦28,800, ₦31,500, ₦35,350, ₦36,550, ₦27,000.
3. Sort a copy, not the table. Click an empty cell, for example F2. In Google Sheets type =SORT(D2:D8, 1, TRUE). In Excel type =SORT(D2:D8). The days appear in order below F2: ₦27,000, ₦28,800, ₦30,600, ₦31,500, ₦33,600, ₦35,350, ₦36,550. (Google's help page writes SORT with two extra parts, 1, TRUE, meaning "sort by the first column, smallest first". Excel sorts smallest first unless you say otherwise.)
4. Count them. There are 7 values. (7 + 1) ÷ 2 = 4, so we want the 4th one.
5. Read the 4th value. It is ₦31,500. Three days took less and three days took more.
6. Check it with one formula. SMALL finds the smallest value, the 2nd smallest, the 3rd smallest, and so on. =SMALL(D2:D8, 4) means "the 4th smallest value in D2 to D8". Type it. It shows ₦31,500. Same answer. (This formula is the same in Sheets and Excel.)
7. Add the edges. =MIN(D2:D8) gives the smallest day, ₦27,000, and =MAX(D2:D8) gives the largest, ₦36,550.

Amara's seven days in order. The amber dot is the middle one: ₦31,500. Synthetic data.

So you can now tell Amara: "Your middle day was ₦31,500. Your days ran from ₦27,000 to ₦36,550." Three numbers instead of seven, and nothing hidden.

Tip. SORT makes a sorted copy and leaves your table alone. That is safer than sorting the table itself (see Watch out).

Tip if you see an error. Some spreadsheets are set up to write decimals with a comma (3,5 instead of 3.5). Those put ; between the parts of a formula instead of ,. If a formula with commas shows an error, try =SMALL(D2:D8; 4).

Your turn, with help

Find Amara's middle day for days 8 to 14 (cells D9 to D15).

Hints: There are 7 days again, so the middle is the 4th in order. Use =SORT(D9:D15, 1, TRUE) in Sheets (or =SORT(D9:D15) in Excel) to see them in order, then check with =SMALL(D9:D15, 4).

Show the answer

The 4th smallest value is ₦33,700. In order, the days are ₦27,100, ₦27,300, ₦30,050, ₦33,700, ₦36,400, ₦37,200, ₦37,700. The smallest is ₦27,100 and the largest is ₦37,700.

Your turn, alone

1. Find the middle day for days 22 to 28 (cells D23 to D29). Also give the smallest and the largest day.
2. Open amara-stall-s1-mangoes.csv (synthetic data). Find the middle weight of the first 5 mangoes (cells B2 to B6). How many of those 5 mangoes are lighter than it?
3. Without a computer: what is the middle position in a sorted list of 11 values?
4. Think: Amara adds an 8th day to her week. Is there still one single middle day? (You do not need to answer fully yet. Lesson 3 does.)

Watch out

• Forgetting to sort. The 4th value in day order (Thursday) only happens to be the middle here. In days 8 to 14 it is not. Always sort first.
• Sorting one column of a table. If you sort column D on its own with the menu, each takings value loses its day: the rows get scrambled. Use SORT in a new place, or sort the whole table together.
• Wrong middle position. For 7 values the middle is (7 + 1) ÷ 2 = 4, not 7 ÷ 2. Count again before you read the answer.

Say it back

1. What must you do to a list of numbers before you can find its middle by eye?
2. A sorted list has 9 values. Which position is the middle?
3. Which formula gives the 4th smallest value in D2:D8?

Show the answers

1. Sort them, from smallest to largest.
2. The 5th, because (9 + 1) ÷ 2 = 5.
3. =SMALL(D2:D8, 4).

What is next

Lesson 2 tests a friend's idea, "add up the week and share it out equally", and finds one day in the month that will surprise you.

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. Days 22 to 28 in order: ₦27,250, ₦27,850, ₦28,950, ₦31,400, ₦31,950, ₦32,750, ₦35,550. The middle (4th) day is ₦31,400 (=SMALL(D23:D29, 4)). Smallest ₦27,250, largest ₦35,550.
2. The first 5 weights in order: 235, 261, 327, 330, 395 grams. Five values, so the middle is the 3rd: 327 grams (=SMALL(B2:B6, 3)). Two of those 5 mangoes are lighter.
3. The 6th, because (11 + 1) ÷ 2 = 6.
4. No. With 8 values there are two middle values, the 4th and the 5th. Lesson 3 shows what to do.