Collecting and organising data

Before you can draw a chart or tell a story with data, you have to collect the data and organise it. This is unglamorous but crucial work , the cleanliness of your data decides the honesty of your conclusions.

Concept

Data is a collection of facts, numbers, measurements, or observations gathered for some purpose. Some examples:

• The favourite fruit of every child in your class.
• The number of pencils each student is carrying today.
• The daily temperature for the past two weeks.
• The result of $30$ throws of a die.

When data is first collected, it is usually a long, messy list , what we call raw data. For example, if you ask $20$ children for their favourite colour, you might get:

red, blue, red, green, yellow, blue, red, blue, green, red, yellow, red, green, blue, red, blue, green, red, blue, yellow.

This is hard to read. To make sense of it, we organise the data , usually into a table.

A frequency table lists each category in one column and the count (frequency) in another. From the colour data:

To count quickly while reading through a list, we use tally marks. Each item is recorded as a small vertical line. Every fifth item gets a diagonal stroke through the previous four, making a "gate" shape:

$\text{||||} \;\text{|}\text{||}\text{||} \rightarrow \cancel{||||}$

A gate stands for $5$. So $13$ becomes "two gates and three lines" , $\cancel{||||} \; \cancel{||||} \; |||$. Tally marks let you record one item at a time without losing count.

After organising, ask: do the frequencies in your table add up to the total number of observations? If not, something is wrong , either a miscount or a missed category.

Worked examples

Example 1. The marks scored by $15$ students in a $5$-mark quiz are: $3, 5, 2, 4, 5, 3, 1, 4, 5, 3, 2, 4, 3, 5, 3$. Make a frequency table.

Example 2. From the table in Example 1, how many students scored at least $4$?

• Scoring at least $4$: marks $4$ or $5$.
• Count: $3 + 4 = 7$.

Example 3. A shopkeeper notes the number of customers each weekday of a week: $25, 30, 28, 35, 40$. What is the total? What is the average?

• Total: $25 + 30 + 28 + 35 + 40 = 158$.
• Average: $158 \div 5 = 31.6 \approx 32$ customers per day.

Example 4. In a die-rolling experiment, $30$ rolls give these outcomes: $2, 4, 6, 1, 3, 5, 2, 4, 6, 3, 1, 2, 4, 5, 6, 2, 3, 4, 1, 5, 6, 2, 3, 4, 5, 1, 2, 6, 4, 3$. Make a tally table.

If the die were perfectly fair, you would expect each outcome $5$ times. Real data wobbles around the expected value.

Try it yourself

1. The number of children in $12$ houses on a lane: $2, 1, 3, 2, 0, 4, 2, 3, 1, 2, 0, 1$. Make a frequency table.
2. From your table in question $1$, how many houses have at least $2$ children?
3. Use tally marks to count this list of letters: A, B, A, C, A, B, B, C, A, C, A.
4. The number of hours of sleep last night for $10$ classmates: $7, 8, 6, 7, 9, 7, 6, 8, 7, 8$. Tabulate.
5. From the previous, what is the average hours of sleep?
6. Take any newspaper. Pick one page and count the number of words "the" in any one paragraph using tally marks.
7. Design: if you wanted to find out the favourite Diwali sweet of your school, how would you collect the data fairly?

Activity

Family survey. Choose a question to ask everyone in your home , for example, "How many glasses of water do you drink in a day?" or "What is your favourite season?". Write down each answer as you ask. Then organise the answers into a tally table and a frequency table. Total the frequencies and check they match the number of people asked.