Functional Skills Qualifications Functional Skills Maths — Handling Data and Statistics Syllabus

Functional Skills Maths — Handling Data and Statistics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Functional Skills Maths — Handling Data and Statistics in Functional Skills Qualifications, not a summary of it.

1. 1

   Collecting and Representing Data

   4 topics

   • Collecting and organising data
     • Tally charts and frequency tables
     • Sorting and grouping data
   • Charts and graphs
     • Bar charts and pictograms
     • Pie charts
     • Line graphs
   • Reading and interpreting tables
   • Choosing the most suitable chart for the data
2. 2

   Averages and Spread

   3 topics

   • Measures of average
     • Mean of a set of values
     • Median and mode
     • Choosing the most appropriate average
   • Range and comparing data sets
     • Calculating the range
     • Comparing two sets using average and range
   • Interpreting and drawing conclusions from statistics
3. 3

   Probability

   3 topics

   • Likelihood and the probability scale
     • Describing events as likely, unlikely or certain
     • Placing events on a 0 to 1 scale
   • Calculating simple probabilities
     • Probability as a fraction, decimal or percentage
     • Equally likely outcomes
   • Listing outcomes and combined events

Functional Skills Maths — Handling Data and Statistics flashcards for Functional Skills Qualifications

24 of 53 cards from the Functional Skills Maths — Handling Data and Statistics deck — real questions with worked answers.

1. What is the difference between primary data and secondary data?

   Primary data is data you collect yourself for your own purpose (e.g. a survey or experiment). Secondary data is data collected by someone else that you reuse (e.g. census results, published statistics).

2. What is the difference between qualitative (categorical) and quantitative data?

   Qualitative/categorical data describes qualities or categories (e.g. colour, gender). Quantitative data is numerical and can be counted or measured (e.g. height, number of cars).

3. What is the difference between discrete and continuous data?

   Discrete data can only take particular separate values, usually whole numbers from counting (e.g. number of pupils). Continuous data can take any value within a range, from measuring (e.g. weight, time, length).

4. What is a data collection sheet (tally chart) used for?

   It is used to record and organise raw data as it is collected, using tally marks grouped in fives, with a frequency column giving the total count for each category or class.

5. How are tally marks grouped, and why?

   Tally marks are grouped in fives — four vertical strokes with the fifth drawn diagonally across them ($\bcancel{||||}$) — so totals are quick and accurate to count.

6. What is a frequency in a data table?

   The frequency is the number of times a particular value, category or class appears in the data set, i.e. the count for that row.

7. What is a grouped frequency table and when is it used?

   A grouped frequency table sorts data into class intervals (e.g. $0\text{-}9, 10\text{-}19$) rather than individual values. It is used when there is a large range or many different values, to keep the table manageable.

8. In a grouped frequency table, why must class intervals not overlap?

   So that every data value belongs to exactly one class. Overlapping intervals (e.g. $0\text{-}10$ and $10\text{-}20$) make it ambiguous which class a value like $10$ goes in.

9. What is a two-way table?

   A table that shows the frequencies for two different categorical variables at once, with one variable in the rows and the other in the columns, and totals along the margins.

10. In a two-way table, what should the row totals and column totals both add up to?

    Both the sum of the row totals and the sum of the column totals must equal the same overall grand total (the total number of items).

11. What does a pictogram use to represent data, and what must it always include?

    A pictogram uses pictures or symbols to represent a quantity. It must include a key stating how many items each symbol represents (e.g. one symbol $= 10$ people).

12. On a bar chart, what does the height (or length) of each bar represent, and how should bars be drawn?

    The height/length represents the frequency. Bars are drawn the same width with equal gaps between them, and the frequency axis must start at $0$ with an even scale.

13. What is the key difference between a bar chart and a histogram?

    A bar chart has equal gaps between bars and is used for categorical/discrete data; a histogram has no gaps between bars and is used for continuous (grouped) data.

14. What does a line graph show, and what type of data is it best for?

    A line graph plots points joined by straight lines to show how a quantity changes, best for showing trends in continuous data over time (e.g. temperature through the day).

15. What does each sector (slice) of a pie chart represent?

    Each sector represents a category's share of the whole; the angle of the sector is proportional to that category's frequency, and the whole circle ($360^{\circ}$) represents the total.

16. How do you calculate the angle for a category in a pie chart?

    $$\text{angle} = \frac{\text{category frequency}}{\text{total frequency}} \times 360^{\circ}$$

17. In a pie chart, if a category makes up $\frac{1}{4}$ of the data, what angle does its sector have?

    $\frac{1}{4} \times 360^{\circ} = 90^{\circ}$.

18. What does a dual (comparative) bar chart allow you to do?

    It places bars for two or more groups side by side for each category, allowing you to compare the groups directly (e.g. boys vs girls for each subject).

19. What is a scatter graph used to show?

    A scatter graph plots paired values of two variables as points to show whether there is a relationship (correlation) between them.

20. In a frequency table, why should you always check that the frequencies add up to the total number of items?

    It is a check for accuracy — if the frequencies do not add up to the expected total, data has been missed or double-counted.

21. When reading a value from a chart with a scale, how do you work out the value of each small division?

    Find the difference between two labelled gridlines and divide by the number of small divisions between them; that gives the value of each small square.

22. Which chart is most suitable for showing how each category compares as a proportion of a whole?

    A pie chart, because each sector shows the fraction/percentage of the total that each category makes up.

23. Which chart is most suitable for showing a trend or change over time?

    A line graph, because joined points clearly show how a quantity rises or falls over time.

24. Which chart is most suitable for comparing the frequencies of separate categories?

    A bar chart, because the heights of the bars can be compared directly.

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