How many loaves is a normal day?: Kofi runs the Market Square shop. Lena asks him a simple question: how many loaves does the shop sell on a normal day? She needs the answer to plan how much Priti's bakers make each night.
Kofi counts every loaf sold for one week in July.
| Day | Mon | Tue | Wed | Thu | Fri | Sat | Sun |
|---|---|---|---|---|---|---|---|
| Loaves sold | 380 | 360 | 400 | 410 | 450 | 630 | 380 |
Seven numbers, and Lena wants one. There are three honest ways to pick a typical value (a measure of the average), and for Kofi's week they give three different answers.
Three ways to find a typical day
The mean: share it out
Add every value, then divide by how many values there are.
380 + 360 + 400 + 410 + 450 + 630 + 380 = 3,010 loaves. 3,010 ÷ 7 = 430 loaves a day.
It is what each day would sell if the week's loaves were shared out evenly.
The median: the middle one
Put the values in order, smallest first, and take the one in the middle.
360, 380, 380, 400, 410, 450, 630. Seven values, so the 4th is the middle: 400 loaves.
With an even number of values there are two in the middle: add them and halve.
The mode: the most common
The value that turns up most often.
380 appears twice, every other number once, so the mode is 380 loaves.
A set can have two modes, or none at all if no value repeats.
Why Saturday pulls the mean up: Saturday's 630 is far above every other day (an extreme value, or outlier). The mean uses every value, so the 630 drags it up to 430, higher than five of the seven days.
The median only looks at the middle position. Make Saturday 900 and the median is still 400; the mean jumps to about 469.
Mean
- Add all values, divide by how many there are
- Uses every value, so nothing is ignored
- Pulled up or down by one extreme value
- Can be a number no day actually sold, like 430
Median
- The middle value once the values are in order
- Not moved by one very high or very low value
- Ignores how big the other values are
- Must be put in order first, or it is wrong
Mode
- The value that appears most often
- Works for words too: the product most customers buy
- There can be two modes, or none
- Ignores every value that does not repeat
The mode is the only one of the three that works for words. When Aisha asks High Street customers what they came in for, the answers are bread, pastries, cakes and sandwiches. There is no mean of 'bread' and no middle of it either, but the most common answer, bread, is the mode.
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Priti's bakehouse makes celebration cakes to order in four sizes. In September it took 40 orders. Writing out 40 prices would be slow, so the order book shows each price once, with how many cakes were ordered at it (the frequency). That is a frequency table.
| Size | Price | Cakes ordered | Price × cakes | Running total of cakes |
|---|---|---|---|---|
| Small | $20 | 5 | $100 | 5 |
| Medium | $30 | 13 | $390 | 18 |
| Large | $45 | 12 | $540 | 30 |
| Extra large | $60 | 10 | $600 | 40 |
| Total | 40 | $1,630 |
The three averages from the table
Mean: multiply, add, divide
Multiply each price by the number of cakes at that price, then add: $100 + $390 + $540 + $600 = $1,630.
Divide by the number of cakes, not the number of sizes: $1,630 ÷ 40 = $40.75 a cake.
Median: count along the running total
40 cakes, so the middle sits between the 20th and the 21st.
The running total reaches 18 after the medium cakes, so cakes 19 to 30 are large. The 20th and 21st are both $45: ($45 + $45) ÷ 2 = $45.
Mode: the biggest frequency
The largest number in the cakes column is 13, for medium cakes.
So the mode is $30, the price. The 13 only tells you which row to read.
Two slips that cost the answer: Averaging the rows. ($20 + $30 + $45 + $60) ÷ 4 = $38.75 treats the 5 small cakes as if they were as common as the 13 medium ones. Each price has to count as many times as it was ordered.
Giving the frequency as the mode. '13' is how many; the mode is the price, $30. Write the $ sign in the working or the answer every time the values are money.
Lena plans a tiered wedding cake at $120 and expects about 6 orders a month. What happens to the mode? Medium cakes still have the biggest frequency, 13 against 6, so the mode stays $30. A new line changes the mode only if it is ordered more often than the current most common one. The mean, which uses every value, would rise.
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Same numbers, faster to read: Lena compares the three shops. In the same July week, before Station Road opened, the mean number of loaves sold a day was 470 at High Street, 430 at Market Square and 350 at Park Road.
Three numbers in a sentence are easy to miss. Drawn as bars, Park Road's gap is obvious at a glance.
A fully labelled bar chart
A title
Say what, where and when: 'Mean loaves sold a day by shop, July 2026'.
The y-axis: a label and a scale
Label it with what is measured and the unit (loaves a day). Start at 0 and go up in equal steps, for example 0, 100, 200 up to 500.
The x-axis: the categories
One bar per shop, each named: High Street, Market Square, Park Road. Bars the same width, with gaps between them.
A key when bars are split
In a stacked bar chart each bar is cut into coloured parts that add up to its total. A key says which colour is which.
A stacked bar chart compares totals and their parts at the same time. Aisha asked 200 High Street customers what they came in for, in September 2025 and again in September 2026. Two bars, one for each year, each 200 customers tall, cut into bread, pastries, cakes and sandwiches. The bread part shrinks from 110 to 90 while the others grow: that shift is the story.
| What customers came in for | Customers | Share of 200 | Angle of the slice |
|---|---|---|---|
| Bread | 90 | 90 ÷ 200 × 100 = 45% | 45% × 360° = 162° |
| Pastries | 50 | 25% | 90° |
| Cakes | 30 | 15% | 54° |
| Sandwiches | 30 | 15% | 54° |
| Total | 200 | 100% | 360° |
A pie chart shows how one whole splits into parts. The whole circle is all 200 customers in September 2026; each slice (a sector) is one answer. To draw it, turn each number into a share of the total, then into an angle: the share times 360°. The angles must add up to 360°. Label each sector with its name and percentage, or use a key, and give the chart a title.
Bar chart
- Compares separate things: shops, products, years
- Height of each bar is the value, on a scale from 0
- Easy to rank and to read off a value
Stacked bar chart
- Each bar is a total, cut into its parts
- Compares both the totals and the mix across years or places
- Needs a key for the parts
Pie chart
- Shows the parts of ONE whole at ONE time
- Slice angle = share × 360°, all adding to 360°
- Hard to read with many small slices, or to compare two pies
One whole, one time: A pie chart answers 'how was this total split?' for one moment. Asked for September 2026, draw 2026 only; two pies, or a chart with both years, answer a different question.
To compare the two years, the stacked bar chart is the one to use.
Lena's window poster: For the Station Road opening in September 2026, Lena puts a poster in every shop window: 'Lena's Bakery in numbers'. No tables and no long sentences: big numbers, small pictures and a few words each.
What the poster shows
- A loaf icon and up to 1,450 loaves baked every night at the Mill Lane bakehouse
- Seven chef's hats: Priti and her six bakers
- A map with four shops: High Street, Market Square, Park Road and, new, Station Road
- A small pie chart: 45% of High Street customers come in for bread
- A wheat sheaf: flour from Valley Grain, the local farmers' cooperative
That poster is an infographic (information shown as a graphic): pictures, icons, big numbers, short text and small charts put together so that one story can be read in a few seconds. Businesses use them in reports, on social media, in shop windows and on the staff noticeboard.
Why a business uses one
- Read in seconds, even by people who would never read a table
- Memorable and easy to share online
- Tells one clear message to customers, staff or investors
What it can hide
- The maker picks the numbers, usually the flattering ones
- Pictures not drawn to scale can make a gap look bigger than it is
- Too little detail to check or calculate anything
- Often no date and no source
Read it like a customer, check it like a manager: 'Up to 1,450 loaves a night' is the busiest night, not a normal one. The mean nightly bake could be well below it, just as Saturday's 630 lifted Kofi's week.
And a loaf icon drawn twice as tall is also twice as wide, so it looks four times as big. Before you trust an infographic, ask who made it, for whom, when, and which numbers are missing.
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How this comes up: A case gives a table, and short parts follow one after another: calculate the mean from it, showing all your working, for two; the median, for two; the mode, with no working, for one; then the effect of a new product on the mode, for one.
Other cases ask for the mean of a list of yearly figures, or how a mean could have been worked out, or for a fully labelled bar chart or pie chart drawn from a table.
The two-mark calculation
- Write the working. From a frequency table: each value × its frequency, then the total. From a list: the sum of the values.
- Divide by the number of items. The total frequency (100 rolls), not the number of rows (4 prices).
- Give the answer with its unit. A $ sign on money, in the working or the answer.
- Check it makes sense. A mean price must sit between the cheapest and the dearest price.
Three traps: Dividing by the rows. ($2 + $3 + $4 + $5) ÷ 4 = $3.50 ignores how many rolls sold at each price.
No $ sign. '3.25' with no $ anywhere loses the answer mark, however right the number.
The frequency as the mode. Asked for the mode, give the value with the biggest frequency, not the frequency itself.
Using Table 1, calculate the mean price of a breakfast roll sold at the Park Road shop on Saturday morning (show all your working).
Model answer plan
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