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Cambridge IGCSE0580

Classifying statistical data

Mathematics 0580 Chapter Notes

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Classifying statistical data
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Classifying statistical data notes

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In this chapter

  1. 1Classifying data into groups
  2. 2Tally tables
  3. 3Adding more data to a table
  4. 4Two-way tables
  5. 5Fractions and percentages in a table

1. Classifying data into groups

To classify data is to sort every item into a group. Each item goes in one group only, and the groups use the words given in the question.

Go through the list once, in order. Count how many items fall in each group. Then add the counts: the total must equal the number of items in the list.

Examiner insight

“Many did not use the words given in the question to complete the table and just completed the frequency column for the tally marks already given.”

Worked example 13 marks

Fifteen students each name a favourite colour: red, blue, blue, green, red, blue, green, red, blue, red, blue, green, blue, red, blue. Sort the data into a table showing each colour and the number of students who chose it.

  1. 1

    Count the colours one at a time, in order.

  2. 2

    red 5, blue 7, green 3 [2]

  3. 3

    check: 5 + 7 + 3 = 15, the number of students, so no item is missed or counted twice [1]

2. Tally tables

A tally table has three columns: the item, the tally and the frequency. Draw one stroke for each item. Every fifth stroke crosses the four before it to make a gate, which stands for 5.

The frequency is the total number of strokes, written as a number. Put marks in the tally column and the number in the frequency column.

Examiner insight

“Common errors included miscounting the number of ‘gates’ giving an answer of 43 or 53, ignoring the incomplete gate and stating 45, or only considering the vertical tallies in each ‘gate’ so giving 39 from 4 × 9 + 3.” “Extra tally marks needed to be clearly shown to gain full marks.”

Worked example 13 marks

The numbers of letters in 12 words are: 3, 5, 4, 3, 6, 3, 5, 4, 3, 5, 4, 4. Complete a tally table with columns for number of letters, tally and frequency.

  1. 1

    Cross out each number as you tally it.

  2. 2

    3 letters: four strokes, frequency 4. 4 letters: four strokes, frequency 4 [1]

  3. 3

    5 letters: three strokes, frequency 3. 6 letters: one stroke, frequency 1 [1]

  4. 4

    total frequency = 4 + 4 + 3 + 1 = 12, the number of words [1]

3. Adding more data to a table

A question may give a table with some results already recorded, then list more. Tally the new data in the tally column. The frequency is then the old count plus the new count for every row.

The new total frequency is the old total plus the number of new results.

Examiner insight

“The most common errors came from not reading the question carefully and only completing the frequency column for the given tallies or completing the frequency column for only the 10 pieces of extra data.”

Worked example 14 marks

The table gives the number of pets owned by 20 students. Ten more students are asked and their answers are 1, 0, 2, 1, 1, 3, 0, 1, 2, 1. Complete the table for all 30 students.

Pets0123
Frequency of the first 206950
  1. 1

    tally the ten new answers: 0 twice, 1 five times, 2 twice, 3 once [1]

  2. 2

    add to the old frequencies: 6 + 2 = 8, 9 + 5 = 14, 5 + 2 = 7, 0 + 1 = 1 [2]

  3. 3

    check: 8 + 14 + 7 + 1 = 30 = 20 + 10 [1]

4. Two-way tables

A two-way table sorts the same data by two features at once, one in the rows and one in the columns. Each cell counts the items with both features. A total sits at the end of each row and column.

Fill in the cells from the totals by subtracting. Then check that every row and every column adds up to its total.

Examiner insight

“Candidates should be encouraged to check that the numbers in each row and column add up correctly to match the totals.”

Worked example 14 marks

There are 60 students. Of these, 35 are girls. In all, 24 students walk to school, and 14 of the girls walk. Complete the two-way table.

BoysGirlsTotal
Walk…1424
Do not walk………
Total…3560
  1. 1

    boys in total = 60 - 35 = 25 [1]

  2. 2

    do not walk in total = 60 - 24 = 36 [1]

  3. 3

    boys who walk = 24 - 14 = 10 [1]

  4. 4

    girls who do not walk = 35 - 14 = 21 and boys who do not walk = 25 - 10 = 15 [1]

  5. 5

    check: 10 + 15 = 25 and 21 + 15 = 36

5. Fractions and percentages in a table

A question may give a total as a fraction or percentage of all the items. Work out the number first, then place it in the correct row or column of the table.

One fifth of 200 is 200 ÷ 5 = 40. Thirty per cent of 200 is 0.3 × 200 = 60. Finish the table by subtraction and check the totals.

Examiner insight

“The common errors included arithmetic errors using the two given values of one fifth and/or 30%, incorrect positioning of these calculated values, and arithmetic errors when completing the rows and/or columns.”

Worked example 14 marks

Do not use a calculator. 200 people visit a café. 30% of them are children. One fifth of all the people order tea. 15 children order tea. Complete the two-way table.

TeaNo teaTotal
Child15……
Adult………
Total……200
  1. 1

    children = 0.3 × 200 = 60 and adults = 200 - 60 = 140 [1]

  2. 2

    tea = 1/5 × 200 = 40 and no tea = 200 - 40 = 160 [1]

  3. 3

    children with no tea = 60 - 15 = 45 and adults with tea = 40 - 15 = 25 [1]

  4. 4

    adults with no tea = 140 - 25 = 115, and 45 + 115 = 160 [1]

Recap

  • Classify data by putting each item in one group, using the words the question gives.
  • Tally table: one stroke per item, every fifth stroke crosses four to make a gate of 5.
  • Frequency = the count, written as a number in the frequency column.
  • New data is added to the old tally: old count plus new count in every row.
  • Two-way table: two features at once. Find missing cells by subtracting from the totals.
  • Fractions and percentages: work out the number first, then place it in the right row or column.
  • Check that the frequencies add to the number of items and that every row and column adds to its total.

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. In a tally table, how many items does one gate (four strokes crossed by a fifth) stand for?1 mark
  2. Do not use a calculator. A tally row has 3 gates and 2 extra strokes. Write down the frequency.2 marks
  3. Do not use a calculator. The colours of 12 cars are: white, black, white, silver, black, white, white, silver, black, white, silver, white. Complete a tally table.3 marks
  4. Do not use a calculator. In 20 matches, the numbers of matches with 0, 1, 2 and 3 goals are 5, 8, x and 2. Find x.2 marks
  5. The table gives the number of brothers and sisters of 22 students. Five more students answer 1, 2, 0, 1, 3. Complete the table for all 27 students. | Brothers and sisters | 0 | 1 | 2 | 3 | | --- | --- | --- | --- | --- | | Frequency of the first 22 | 7 | 11 | 4 | 0 |3 marks
  6. Do not use a calculator. 40 students each study French or Spanish. 18 are boys. 25 study French, 11 of them boys. Complete the two-way table. | | Boys | Girls | Total | | --- | --- | --- | --- | | French | 11 | … | 25 | | Spanish | … | … | … | | Total | 18 | … | 40 |4 marks
  7. 150 club members each choose one activity. Complete the two-way table. | | Swim | Run | Cycle | Total | | --- | --- | --- | --- | --- | | Under 18 | 23 | 31 | … | 70 | | 18 and over | 28 | … | 19 | 80 | | Total | … | … | … | 150 |5 marks
  8. Do not use a calculator. 120 people use a gym. One fifth are juniors and 30% are seniors. The rest are adults. 75 people are members, including 18 juniors and 21 seniors. How many adults are not members?4 marks
  9. Amir asks 100 workers how they travel to work. His tally table has Car: 9 gates and 3 strokes. Bus: 5 gates and 4 strokes. Walk: 2 gates and 1 stroke. The only other row is Cycle. Then 15 more workers answer: 6 Car, 4 Bus and 5 Cycle. Write the tally for Cycle for all 115 workers as gates and strokes.5 marks
  10. Do not use a calculator. 240 visitors to a museum are each a child, an adult or a senior. Each buys a day ticket or a season ticket. 45% of the visitors are adults. One sixth of the visitors are seniors. Three eighths of all the visitors buy a season ticket. 52 children buy a day ticket. 14 seniors buy a season ticket. Work out how many adults buy a day ticket.6 marks

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