Putting data in order

Sushri Sandhya asks her students their shoe sizes and writes all 27 numbers on the board in the order the students answer: 4, 5, 3, 4, 3, 4, 5, 5, … In that jumbled order, even simple questions like 'What is the largest size?' are hard.

So she arranges the sizes in ascending order, from the smallest to the largest: 3, 3, 3, then nine 4s, then ten 5s, then four 6s, and finally one 7. Now equal sizes sit together.

See how easy the questions become:

• The smallest size is the first number: 3.
• The largest size is the last number: 7.
• The 5s are all together, so we count them at once: 10 students wear size 5.
• Sizes larger than 4: count everything after the last 4: ten 5s, four 6s and one 7, so 10 + 4 + 1 = 15 students.

If the school orders shoes, it can now tell the shopkeeper exactly which sizes to send, and how many of each.

Arranging data in order is a simple way to organise it. It does not change the data; it just puts it where our eyes can find things quickly.