Data Handling
ICSE Class 7 · Mathematics · Chapter 21
What this chapter covers
- Data and why it is collected
- Choosing data to test a hypothesis
- Organising data: tally marks and frequency tables
- Representative values
- The mean
- The median
- The mode
- Choosing the right average
- Constructing a bar graph
- Reading and interpreting bar graphs
Key points
- Data is a collection of facts gathered to give information; each single value is an observation.
- A hypothesis is a statement that can be checked by collecting the right data; collect only the data that tests it.
- Tally marks, grouped in fives, and a frequency distribution table organise raw data; the frequencies must add up to the number of observations.
- Mean = Sum of observations ÷ Number of observations; it is the equal share of the total.
- Sum of observations = Mean × Number of observations, which helps find a missing value.
- The median is the middle value of the ordered data; for an even number of observations it is the mean of the two middle values.
- The mode is the value that occurs most often; data can have one mode, more than one mode, or none.
- The mean is pulled by extreme values, the median is not, and the mode is the only average for non-numerical data.
- A bar graph uses bars of equal width and equal gaps, with lengths proportional to the values; the scale must be stated and the axis must start at 0.
- Reading a bar graph turns bar lengths back into numbers; inferences from it are careful guesses, not certainties.
Questions answered
What is the difference between raw data and data arranged in a frequency distribution table?
Raw data is in the form in which it was first collected, in no particular order. A frequency distribution table lists each value or category with the number of times it occurs, so the data can be read and compared quickly.
Find the mean of 4, 9, 11, 16 and 20.
Sum = 60, number of observations = 5, so the mean = 60 ÷ 5 = 12.
Find the median of 23, 17, 31, 19, 26 and 28.
In ascending order: 17, 19, 23, 26, 28, 31. There are 6 values, so the median is the mean of the 3rd and 4th: (23 + 26) ÷ 2 = 24.5.
Find the mode of 2, 3, 3, 5, 3, 6, 5.
3 occurs three times, more than any other value, so the mode is 3.
The mean of six numbers is 15. Five of them are 12, 18, 10, 20 and 14. Find the sixth number.
Sum of six numbers = 15 × 6 = 90. Sum of five = 74. Sixth number = 90 - 74 = 16.
In a small office, four clerks earn ₹15,000 a month each and the manager earns ₹95,000. Which average, mean or median, better describes what a typical worker earns? Give a reason.
The median, ₹15,000. The mean is (4 × 15000 + 95000) ÷ 5 = ₹31,000, which is pulled up by the one large salary and is more than four of the five people earn.
True or false: the mean of a set of data is always one of the observations.
False. The mean of 1, 2, 4 and 5 is 3, which is not one of the observations.
The largest value to be shown on a bar graph is 64, and the vertical axis can be at most 10 cm long. Suggest a suitable scale and give the height of the tallest bar.
1 cm to 8 units is suitable. The tallest bar is 64 ÷ 8 = 8 cm, which fits within 10 cm.