Analysis & explanation — cards that explore how a result changes and put a calculation into words

The four cards on the left are inputs: a price of $8, materials of $2, 50 items sold and a stall fee of $50. The three in the middle are calculations: profit per item $6, profit on sales $300, and $250 left over. The two on the right are cards from this page. Both are connected to "Left over".

• "Explain in words", top right, writes the calculation that leads to the amount left over as three sentences.
• "Scenario table", bottom right, lists the amount left over with the number of items sold at its low, base and high values.

With the price set to 10, the sentences are rewritten at once, and the first one becomes "Subtract Materials $2 from Price $10 to get Profit per item $8". The amount left over is $350. The scenario table does not recompute by itself; the card asks for "Compute" to be pressed again. After that, the table shows $190, $350 and $590.

Sensitivity

Given one result card, it moves each input of that calculation a little, one at a time, and shows how much the result changes as bars. The step is one of "1%", "5%", "10%", "20%" and "50%", and the bars appear when you press "Compute". Up to eight bars are shown, the largest change first. It does not recompute when an input changes later; the card asks for "Compute" to be pressed again.

The inputs it moves are input cards and calculation cards that hold just a number. They are included when the connected result uses them, even through other calculation cards. This card does not pass a value on to other cards. How to read the bar colours, and what to check when it does not work, is in the usage guide under Visualize, in the section on "Sensitivity".

Open a board with a Sensitivity card ↗

What if I move it? (sweep)

Given one result card, it moves one input across a range and draws how the result changes as a curve. On the card you choose the input under "Move", the lower and upper ends of the range, and the number of points ("20 pts", "40 pts" or "80 pts"), then press "Draw". When the curve has a peak or a valley, the card shows the maximum or minimum; where it crosses 0, it shows the input values there.

After drawing, changing the input being moved moves a dot along the curve. Changing any other input redraws the curve; when redrawing takes too long, the card asks for "Draw" to be pressed again. This card does not pass a value on to other cards either. The starting range and how redrawing works are in Visualize, in the section on "What if I move it?".

Open the percentage change board with a sweep card ↗

Pile up & clear

When the same amount comes in each time and up to a fixed amount can be handled each time, this card counts how much is waiting after each time. It fits stock on a shelf, a backlog of work or a queue at a till. The numbers are typed into its four fields; they cannot come from other cards through a connection.

• "Start amount" — how much is waiting at the start
• "In each time" — how much comes in each time
• "Handled each time" — the most that can be handled each time
• "Times" — how many times to count (1 to 120)

Each time, the amount coming in is added first, and then up to the handled amount is taken away. When less is waiting than can be handled, only what is there is handled, so the amount never goes below 0. The large number is what is waiting after the last time. Connected to another card, it passes this number on.

Board 2 has 30 open requests, 5 new ones a day, and up to 8 handled a day. One time is one day. The requests go down by 3 a day and reach 0 on day 10. Times is 12, so the large number is 0 requests. The line on the right is a chart card connected to this card; it shows the number of requests from time 0 to time 12.

With Times set to 5, the large number is 15 requests. With Times back at 12 and "Handled each time" set to 6, the requests go down by only 1 a day, and 18 are still open after 12 days. With "Handled each time" set to 4, more comes in than is handled, and the requests grow to 42 after 12 days.

With 8 handled each time, the small text under the large number reads as follows.

• "Peak 30 requests (time 0)" — the time when the most was waiting, and how much. On Board 2 the first 30 requests are the most, so it is time 0.
• "Clears in up to 4" — the longest it takes for anything that came in to be handled, counting the oldest first. On Board 2, the first 30 requests are all handled by day 4. A note under it says this is the longest, not the average.

When something is still waiting at the end of the count, the card shows "Clears in 4+" with a plus sign. This is what happens with Times set to 5. When the start amount is 0 and at least as much can be handled as comes in, nothing waits, and the card says "Nothing piles up".

The small picture in the card shows the total that has come in (the blue line) and the total handled (the grey line). The gap between the two lines is how much is waiting at that time. A negative number in a field becomes 0. Times is rounded to a whole number, and anything above 120 becomes 120, with a notice.

Explain in words

Given one result or formula card, it writes the calculation that leads to its value as sentences, one step each. It follows the formulas back from the connected card and lists the steps from the one closest to the inputs. This card does not pass a value on to other cards.

With Board 1 as it opens, the explanation of "Left over" is these three sentences.

1. Subtract Materials $2 from Price $8 to get Profit per item $6
2. Multiply Profit per item $6 and Items sold 50 items to get Profit on sales $300
3. Subtract Stall fee $50 from Profit on sales $300 to get Left over $250

The shape of each sentence depends on the formula in that calculation card.

• A subtraction or division of two numbers — "Subtract B from A", "Divide A by B"
• A formula that only adds or only multiplies — "Add A and B", "Multiply A and B"; with three or more, they are joined with "and".
• Any other formula — one with brackets, for example, is written out with the card names and values, after "Compute".
• An input card connected directly — a single sentence such as "Price $8 is a plain value".

Names, values and units appear as they do on the cards, and the sentences change as soon as a number changes. "Copy" at the bottom right copies the text, one sentence per line.

When the calculation has many steps, the card shows the first twelve from the inputs and the step of the connected card, followed by a note that it was cut. When the connected card shows an error, the card says so. If a second card is connected, the explanation is still of the first one.

Scenario table

Given result cards, it works out the whole board with low, base and high values and lists the results in a table. The table lists up to twelve connected cards, one row each, in the order they were connected. This card does not pass a value on to other cards.

The low and high values are kept in input cards.

1. Pressing "⋯" (Card menu) at the top right of an input card and choosing "Add scenario values" adds "Low" and "High" fields under the card. Right-clicking the card opens the same menu.
2. "Open fields" on the scenario table adds these fields to every input card that the connected results use. The button is there while no input card on the board has low or high values.
3. Typing "±10%" or "±100" in a field fills both, around the current value: the smaller one in "Low" and the larger one in "High".

The base value is the input card's usual value. An input with empty low and high fields uses its base value in all three. On Board 1 only the number of items sold has values: low 30 and high 80. With Board 1 as it opens, the table shows the amount left over with 30, 50 and 80 items sold: $130, $250 and $430.

"Low" and "High" are the names of the fields; nothing decides which one holds the larger value. "±10%" puts the smaller value in "Low", so for an input where more is worse, such as a cost, retyping the two fields keeps the table pointing the same way.

The table is made when you press "Compute". If any input card has low or high values, it is also made once when the board opens. It does not recompute when an input changes later; the card asks for "Compute" to be pressed again. While no input card has low or high values, no table is made and the card asks for them. When the connected results use no input card at all, the card says so.

When a board opened in CalcAnyway has input cards with low or high values, a "Scenario" switch appears at the top of the screen. Pressing "Low" works out the whole board with the low values, and the calculation cards change to match. An input card keeps its large number and highlights the low field in use; the table highlights the selected column. The switch does not appear in a board embedded in a page like this one.

Articles that use these cards

• Percentage change — a "What if I move it?" card draws the rise needed to get back as the fall changes.

Read next — Equations & formulas Cards that solve equations and systems of equations, and cards for fractions, statistics and other formulas.

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