Data Handling
ICSE Class 8 · Mathematics · Chapter 22
What this chapter covers
- Data and why it needs organising
- Arranging ungrouped data into groups
- Frequency distribution tables
- Bar graphs of grouped data
- Reading pie charts
- Drawing pie charts
Key points
- Data is a collection of facts gathered to give information; each single value is an observation.
- Raw data is data as first collected; when there are many different values, grouping makes it easier to read.
- The range is the largest observation minus the smallest.
- A class interval has a lower limit and an upper limit; the class size is their difference.
- In exclusive form, a value equal to a class's upper limit is counted in the next class.
- Tally marks, drawn in bundles of five, help count observations into classes without missing any.
- The frequency of a class is the number of observations in it; the frequencies must add up to the total number of observations.
- In a bar graph of grouped data, the bars stand on the class intervals, have heights equal to the frequencies, and touch each other.
- A pie chart shows parts of a whole as sectors of a circle; the whole circle is 360° or 100%.
- Central angle = (value)/(total) × 360°, and 1% of a pie chart is 3.6°.
- Value of a sector = (central angle)/(360°) × total.
- Use a pie chart for a share of a whole, and a bar graph of grouped data for how many observations fall in each group.
Questions answered
What is the difference between raw data and grouped data?
In raw data, every observation is listed separately, exactly as it was collected and in no order. Grouped data sorts the observations into class intervals and records only how many fall in each interval.
The ages, in years, of the people at a fictional village meeting range from 18 to 73. Find the range.
Range = 73 - 18 = 55 years.
For the class interval 45–50, write the lower limit, the upper limit and the class size.
Lower limit 45, upper limit 50, class size 50 - 45 = 5.
In a table with classes 10–20, 20–30 and 30–40, in which class is the observation 20 counted? Why?
In 20–30. In exclusive form, a value equal to the upper limit of a class is counted in the next class, so 20 does not belong to 10–20.
The daily rainfall, in mm, on 20 monsoon days in a town was: 12, 5, 27, 18, 33, 8, 21, 15, 2, 29, 24, 11, 36, 19, 7, 25, 14, 31, 22, 16. Make a frequency distribution table with classes 0–10, 10–20, 20–30 and 30–40.
0–10: 4 days (5, 8, 2, 7). 10–20: 7 days (12, 18, 15, 11, 19, 14, 16). 20–30: 6 days (27, 21, 29, 24, 25, 22). 30–40: 3 days (33, 36, 31). Total = 4 + 7 + 6 + 3 = 20.
Why are the bars of a bar graph of grouped data drawn touching each other?
The class intervals follow one another without a break, since each class ends where the next begins. Touching bars show that the values run on continuously.
A pie chart shows how 1,200 people travel to work. The sector for bus has a central angle of 75°. How many people travel by bus?
(75)/(360) × 1200 = 250 people.
A sector of a pie chart stands for 35% of the data. What is its central angle?
35 × 3.6° = 126°.