Collecting Data, Tally and Frequency Tables
Collecting data is the first stage of a statistical investigation: deciding what information is needed, then gathering it either as primary data, collected firsthand for a specific investigation, or secondary data, which already exists, such as a published report. A tally chart records data as it is collected using a single stroke for each item, grouped into fives, and its totals are organised into a frequency table, grouped into equal-width class intervals, written as 0 <= h < 10, when data spans a wide range of values.
Before you start
No specific prerequisites - this is a good place to start.
Method
- Decide whether the data already exists somewhere (secondary data) or needs to be collected specifically for this investigation (primary data).
- Design a data collection sheet or tally chart with clear categories, or class intervals, before collecting anything, so nothing gets left out and nothing gets recorded twice.
- Record each piece of data with a single tally stroke in the matching row, grouping strokes into fives (four single strokes, then a fifth drawn diagonally across them, like a small gate) to make large totals quick and easy to count.
- Convert each row's tally into a frequency by counting the complete groups of five and adding any extra strokes, then total the frequency column to check it matches the number of items actually collected.
- For continuous data, or data spread across a wide range of values, decide sensible EQUAL-width class intervals for a grouped frequency table, using inequality notation such as 0 <= h < 10, so intervals never overlap and every value fits into exactly one class.
- Classify each variable as it is collected: qualitative (categorical) data is a label or category, such as favourite colour, while quantitative data is numerical and is either discrete (only certain values are possible, such as a whole number of pets) or continuous (any value is possible, such as a height or a time).
- Check the finished table: a sensible number of rows or classes, no gaps or overlaps between class intervals, and a total that matches the amount of data collected.
Worked example
A student records the type of vehicle passing the school gate over 10 minutes. Her tally shows: Car, two complete groups of five plus one extra mark; Van, one complete group of five plus three extra marks; Bus, two extra marks and no complete groups; Bicycle, one complete group of five plus four extra marks. Construct a frequency table from this tally, and find the total number of vehicles recorded.
- Convert Car's tally: 2 complete groups of five (2 x 5 = 10) plus 1 extra mark = 10 + 1 = 11.
- Convert Van's tally: 1 complete group of five (5) plus 3 extra marks = 5 + 3 = 8.
- Convert Bus's tally: no complete groups, just 2 extra marks, so Bus's frequency is 2.
- Convert Bicycle's tally: 1 complete group of five (5) plus 4 extra marks = 5 + 4 = 9.
- Write the frequency table: Car 11, Van 8, Bus 2, Bicycle 9.
- Add the frequencies to find the total: 11 + 8 + 2 + 9 = 30 vehicles were recorded in total.
Practice questions
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Q1A student wants to know how many hours of sunshine his town had last month. He looks up the figure on a weather website rather than measuring it himself. Is this primary or secondary data?Show answer
Answer: Secondary data (it already existed and was collected by someone else; he is simply looking it up, not measuring it himself)
Q2State whether the wingspan of butterflies caught in a trap is discrete or continuous data.Show answer
Answer: Continuous data (a wingspan can take any value, including decimals, such as 4.7 cm, not just whole numbers)
Q3While recording pupils' favourite ice cream flavours, a student tallies the votes for Chocolate as three complete groups of five, plus four extra marks. How many pupils chose Chocolate?Show answer
Answer: 19 pupils (3 x 5 = 15, plus 4 extra marks, 15 + 4 = 19)
Q4A tally for the votes cast for Strawberry shows two complete groups of five and no extra marks. Write this as a frequency, and explain in words what a complete group of five looks like on a tally chart.Show answer
Answer: 10 (2 x 5). A complete group of five is drawn as four single vertical strokes, with a fifth stroke drawn diagonally across them like a small gate, which makes groups of five quick to count
Q5A shop records the age, in years, of 30 customers buying a birthday card, ranging from 8 to 82. Suggest one suitable, equal class width for a grouped frequency table, and write the first class interval using inequality notation, starting the first class at 0.Show answer
Answer: A class width of 20 works well, giving the first class interval 0 <= a < 20 (a width of 10 would also be acceptable, as long as every class is the same width and the intervals do not overlap)
Q6State whether favourite school subject, collected from a class of pupils, is qualitative (categorical) data or quantitative data.Show answer
Answer: Qualitative (categorical) data, because it is a label or category, such as Maths or Art, rather than a number
Q7A tally for the number of pieces of fruit eaten by 24 pupils in one day shows: 0 pieces, one complete group of five; 1 piece, two complete groups of five; 2 pieces, one complete group of five plus two extra marks; 3 pieces, two extra marks. Find the frequency for '2 pieces', and state how many of the 24 pupils ate at least 2 pieces of fruit.Show answer
Answer: Frequency for 2 pieces = 5 + 2 = 7. At least 2 pieces = 7 + 2 = 9 pupils (checking: 5 + 10 + 7 + 2 = 24, which matches the 24 pupils given, confirming the tally has been read correctly)
Q8Explain why it is important to design a data collection sheet with clear categories before starting to collect data, rather than while collecting it.Show answer
Answer: If the categories are not decided in advance, some data collected early on might not fit the categories chosen later, meaning it would need to be collected again or discarded, and different people collecting data might record the same item inconsistently
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
A gardener records the mass, in kg, of 28 marrows grown on his allotment this year, using a tally chart with three class intervals: 0 <= m < 4 kg, two complete groups of five; 4 <= m < 8 kg, three complete groups of five; 8 <= m < 12 kg, three extra marks and no complete groups. (a) Complete the frequency table shown by the tally. (b) State the class width used for each interval. (c) A friend suggests using the class intervals 0 <= m < 4, 3 <= m < 8, 8 <= m < 12 instead. Explain why this would NOT be a suitable set of class intervals for a grouped frequency table.
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A student is investigating how long pupils in her year group take to travel to school. (a) She decides to time 30 pupils' journeys herself using a stopwatch, rather than using data the school already holds. State whether this is primary or secondary data, and give one reason for your answer. (b) State whether journey time is discrete or continuous data, and give one reason for your answer. (c) She wants to record her results in a grouped frequency table with class intervals of equal width 10 minutes, starting at 0 minutes. Write down the first TWO class intervals, using inequality notation.
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A cafe manager tallies the number of hot drinks sold in an hour: Tea, two complete groups of five plus one extra mark; Coffee, three complete groups of five plus four extra marks; Hot chocolate, one complete group of five. (a) Find the frequency for each drink. (b) Given that a total of 35 hot drinks were sold in the hour, use this to check your frequencies are correct.
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Free printable worksheet
Want more practice on paper? Download the collecting data, tally and frequency tables worksheet pack - 9 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 30 of KS3 Maths Workbook 2, the whole course as one free printable PDF.
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