Classifying statistical data
Section: Statistics | Syllabus: Cambridge IGCSE Mathematics (0580)
Types of Statistical Data
- Qualitative data is non-numerical, describing a quality or category (e.g. favourite colour, type of pet, opinion)
- Quantitative data is numerical, and splits into two further types:
- Discrete data can only take specific, separate values, usually found by counting (e.g. number of siblings, number of cars)
- Continuous data can take any value within a range, usually found by measuring (e.g. height, time, mass)
- Data can also be primary (collected first-hand by the person carrying out the investigation) or secondary (already collected by someone else and re-used)
Worked Example: Classifying Data
- Question: For a class survey, classify each variable as qualitative, quantitative discrete, or quantitative continuous: (a) favourite subject, (b) number of pets owned, (c) height of each student in cm.
- (a): favourite subject is non-numerical, so it is qualitative
- (b): number of pets is counted in whole numbers, so it is quantitative discrete
- (c): height can take any value within a range (e.g. 152.3 cm), so it is quantitative continuous
Common Mistakes
MistakeAssuming data is continuous just because the values contain decimals (e.g. money, which is counted in fixed steps of the smallest coin)
Fixthe deciding factor is whether every value in a range is possible (continuous) or only specific, separate values are possible (discrete) - not whether decimals appear
MistakeDeciding discrete vs continuous based only on whether the data was "counted" or "measured", without checking if every in-between value is actually possible
Fixcounting vs measuring is a useful hint, but the real test is whether the variable could take any value in a range (continuous) or only fixed, separate values (discrete)
Tabulating Data: Frequency Tables
- Raw data can be collected using a tally chart, then converted into a frequency table showing each value alongside how many times it occurs
- A frequency table makes a large set of raw data much easier to read and use for further calculations
Worked Example: Constructing a Frequency Table from Raw Data
- Question: The number of siblings for 15 students is recorded: 0,2,1,3,0,1,1,2,4,0,1,2,3,1,0. Construct a frequency table, and state how many students have more than 2 siblings.
- Step 1: Count how many times each value occurs
Number of siblings 0 1 2 3 4 Frequency 4 5 3 2 1 - Step 2: "More than 2 siblings" means 3 siblings or 4 siblings: 2+1=3
- Answer: 3 students have more than 2 siblings
- Step 1: Count how many times each value occurs
Common Mistakes
MistakeLosing track of the raw data count part-way through tallying, giving frequencies that do not add up to the total number of items
Fixalways check that the frequencies in the finished table add up to the total number of data values collected
MistakeMisreading "more than" as "at least", including the boundary value itself
Fix"more than 2" means strictly greater than 2 (so 3, 4, ...), while "at least 2" would include 2 itself - read the wording carefully
Grouping Continuous Data into Class Intervals
- Continuous data (e.g. mass, time, length) can take infinitely many values, so it is grouped into class intervals for a frequency table
- Class intervals are usually written using inequality notation, e.g. 10 m<15, meaning m can be any value from 10 up to (but not including) 15
- Class intervals must not overlap, and together they must cover the whole range of the data with no gaps
Worked Example: Reading a Grouped Frequency Table
- Question: 20 parcels are weighed and grouped by mass, m kg, as shown.
How many parcels weigh less than 10 kg?Mass, m (kg) 0 m<5 5 m<10 10 m<15 15 m<20 Frequency 6 8 4 2 - Step 1: "Less than 10 kg" covers the first two class intervals, 0 m<5 and 5 m<10
- Step 2: Add their frequencies 6+8=14
- Answer: 14 parcels weigh less than 10 kg
Common Mistakes
MistakeWriting class intervals that overlap at the boundary, e.g. 0 m5 followed by 5 m10, so a value of exactly 5 could belong to either interval
Fixuse a strict inequality on one end of every interval (such as <) so each value belongs to exactly one class interval
MistakeAssuming every class interval must have the same width
Fixequal class widths are common and convenient, but the only strict requirements are that intervals do not overlap and cover the full range with no gaps
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