How was the data collected?

The idea

Understanding how data is collected or produced shows its scope and limitations, such as bias or missing information, and how confidently conclusions can be drawn from it.

What does 38 °C mean?

A graph says that Punjab's maximum temperature in June was 38 °C. Weather stations in a few places across the state record the temperature.

What does the 38 °C mean?

• Every place in Punjab was 38 °C all through June
• The highest value recorded at any weather station in June
• The average temperature of the state in June

Who do we ask?

Which sport do the 100 children of a school like best? Ask each group, look at the graph it gives, then compare the three.

Know how it was collected

Understanding how data is collected or produced shows its scope and limitations, such as bias or missing information, and how confidently conclusions can be drawn from it.

The cricket-ground group said 80% like cricket. The whole school said 40%. The answer depended on who was asked. That group was biased: it was mostly cricket lovers.

The book gives more examples. A state's maximum temperature for a month is the highest value among all its weather stations, not the temperature everywhere. Average rainfall for June is the June rainfall averaged over a few years, not the rain of one year.

Data can also have missing information. In the book's graph of objects launched into space, the counts of three countries do not add up to the worldwide count. Other countries are not shown.

Notes

Understanding how data is collected or produced shows its scope and limitations, such as bias or missing information, and how confidently conclusions can be drawn from it.

Check yourself

A graph says Kerala's maximum temperature in April is 33 °C. What does this mean?

Chennai's June rainfall in four years was 40 mm, 60 mm, 50 mm and 70 mm. The graph shows the monthly average for June. What value does it show, in mm?

Answer: 55

(40 + 60 + 50 + 70) ÷ 4 = 220 ÷ 4 = 55 mm. It does not say what any one year was.

A graph shows 2800 objects launched worldwide in a year. Three countries are shown, with 1200, 500 and 400. How many objects were launched by the countries not shown?

Answer: 700

1200 + 500 + 400 = 2100. The worldwide count is 2800, so 2800 − 2100 = 700 objects are from countries not shown.

A principal wants to know how children travel to school. She asks only the children who arrive by school bus. What is wrong?

• Every place in Kerala was exactly 33 °C in April. The maximum is not the temperature everywhere. Some places were cooler.
• The average temperature of the whole month of April. An average would be lower than the maximum. The maximum is the highest reading.
• The temperature at one place on 1 April. It is not the reading of one day. It covers the whole month and the whole state.
• The highest value recorded by any weather station in the state in April — correct. Yes! The monthly maximum is the highest of all the values the weather stations recorded.
• Nothing, she asked enough children. Asking many children does not help if the group is not like the whole school.
• She asked only one group, so the data is biased and misses children who walk or cycle — correct. Yes! Everyone she asked came by bus, so the graph shows only buses.
• She should ask only the children who walk. That would be biased in the other direction. She should ask children from every group.
• She should ask fewer children. Fewer children would not remove the bias. She needs children from all groups.