Data Handling and Bar Charts

1Summary 重點摘要

Organize data, draw bar charts, frequency tables.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Collect data — know what you're askingBefore collecting data, decide exactly what you want to find out, for example 'Which fast food does the class like best?' Then ask each classmate in turn and record every answer. What you gather is called raw data; before it is organised it is just a messy list, such as: chicken, burger, fish ball, burger, burger, chicken, fish ball, burger, burger, chicken. Ask the question concretely — 'which one do you like best' rather than 'what do you think' — so answers fall into clear categories; fixing the options in advance, say burger, chicken or fish ball only, makes organising easier still.
2. Step 2: Make a frequency table — use tally marksRaw data is messy, so organise it into a frequency table. The method is direct: list every category, then count how many times each one appears; that count is the frequency, and tally marks are a handy way to keep count. In the example above, burger appears 5 times, chicken 3 times and fish ball 2 times. Once the table is done, the most popular choice is obvious at a glance. After counting, verify: the frequencies should add up to the class size, 5 + 3 + 2 = 10; any mismatch means an answer was missed or counted twice.
3. Step 3: Draw a bar chart — axes setupA bar chart has two axes: the X-axis (horizontal) carries the categories, such as burger, chicken and fish ball, while the Y-axis (vertical) carries the frequencies, that is, the counts. Draw one bar for each category, with the height matching its frequency: burger has 5, so its bar reaches 5; chicken has 3, so its bar reaches 3. The heights must be accurate. Keep every bar the same width and evenly spaced; if each Y-gridline stands for 1 student, the burger bar covers 5 gridlines. With larger frequencies each gridline may stand for 2 or 5, and the bar heights are scaled accordingly.
4. Step 4: Gaps between bars — key difference from histogramsBar charts and histograms are different kinds of statistical chart, and exams often test the difference. The key point: the bars of a bar chart must have gaps between them, because the categories are separate and not continuous. In a histogram the bars touch with no gaps, because it handles continuous data such as weight or height. Remember this well and do not mix them up. A quick test: if the X-axis carries category names (burger, chicken) it is a bar chart; if it carries continuous intervals (such as 40 to 45 kg) it is a histogram. Read the X-axis before naming the chart.
5. Step 5: Title and labels — don't skipDrawing the bars is not the end. A proper bar chart must include three things: a title at the top, such as 'Favourite fast food of the class'; a label on the Y-axis saying 'Frequency'; and a label on the X-axis saying 'Type of fast food'. A chart without labels is incomplete, readers cannot tell what each bar means, and marks are lost in exams for exactly this reason. The title should state what the data are and when they were collected, such as 'Favourite fast food of our class, October'; marking the frequency at the top of each bar lets readers read the numbers directly.
6. Step 6: Read the chart — most and leastOnce the chart is drawn you can interpret it: the longest bar shows the most popular choice, and the shortest bar shows the least popular. In the example, the burger bar is the longest, so burgers are the most popular; the fish ball bar is the shortest, so fish balls are the least popular. You can also compare: how many more students like burgers than fish balls? 5 - 2 = 3, that is, 3 more. Go further with proportions: burger-lovers make up 5 ÷ 10 = 50% of the class, one half; the value of a statistical chart lies in turning messy raw records into conclusions seen at a glance.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Data collect must organize frequency table
• Tally mark most convenient
• Bar chart bars must have gaps
• Chart must have title and axis name
• Longest bar most, shortest bar least