Exploring Data Visually

Read a bar chart the way a person actually questions one: how much is this bar, about how much when its top sits between ticks, which is the most, which is most like this one, which two, and which bar holds a given value. One figure of one weather station's rain grows from four bars to seven on a single axis, is sorted, and is turned on its side - with a reading ruler you drag to a bar's top, and the mistake this lesson exists to catch: counting gridlines instead of reading the axis.

Compare two bars: a difference is a length you read on the axis, not an impression you get from the bars. Stretch a gap bracket between two bar tops and read its length; tap the pair that is farthest apart; stack the short bar until the tops meet to find a multiple. And the mistake this lesson exists to catch: an axis that does not start at zero, where one bar looks twice the other and the gap is ten.

A slice is a share of one whole. Sweep a slice edge to edge and a percent rim counts its share; the whole itself is written nowhere on the slices, which is how a pie misleads. One weather station's year, a spring that reverses the eye's judgment, a crowded disc read through its legend, and two golden cuts you drag to build a year of your own - then three checks in a merchant's hold, one submission each.

A bar is a stack of days. Three hundred and sixty daily highs rain into ranges of the thermometer and stack; a gold bracket dragged across the bins counts the days between two edges; the axis on the left counts days, not degrees, which is how a histogram misleads. One weather station's year, a tallest bar that is not the hottest day, a dial that turns the year to noise or a blob until the shape shows - then three checks in a clinic's waiting room, one submission each.

A percentile is a rank, not a size. A luminous cut dragged along the year's daily highs lights every day below it and counts them; that count over the whole is the rank. Find the median and the quartiles, bracket the middle half, watch the eightieth percentile refuse to mean eighty per cent of the hottest day, and see the ranks crowd where the days crowd - then three checks in a clinic's waiting room, one submission each.

One world, every figure of the level. Marta's bakery, four weeks of loaves: rule a day's bar and read the amount, stretch a bracket for the difference, sweep a slice for the share and take it of the whole, bracket the histogram's bins for a count and a threshold, cut the month for a day's rank. Fifteen boards, no scaffolds, one submission each - and the level's judgement: which figure answers which question.

A boxplot is a month folded to five numbers. Twenty-eight dawn readings of a mountain river fall onto the gauge, split into quarters, and become a box: tap its line and edges and read them, place the golden pins where a quarter and half of the dawns lie, bracket the box to name the interquartile range, then watch a second month's narrow box refuse to hold fewer days. What a box says, what it hides, and three checks in chalk on a class's scores, one submission each.

Four months of the river on one gauge. Two more months fall in as drops and fold into boxes beside April and June; then the comparing begins: tap the two steadiest, watch the eye follow the longest whisker to the wrong month and the boxes light up to correct it, reach from line to line for the difference, bracket the overlap, find the box that leans, stand the four on gauge posts, and put the months in order by their lines. Then three classes in chalk, one submission each: the same line is not the same class.

Twelve months of the river as twelve standing boxes on one gauge: the season is a shape. Tap the peak and the restless month, reach from March's line to April's for the melt, tap the two months of the biggest fall, watch the eye take the widest box for the biggest rise and the golden curve through the twelve lines correct it, mark the high season, choose between the curve alone and the row of boxes, and find every step downhill. Then a class's twelve tests in chalk, one submission each.

One world, every figure of the level, one submission each. The Skerry ferry, passengers on the morning crossing: fold April into a box and read its line and its width; count what a box holds whatever its width; compare four months by their boxes and never their whiskers, reach line to line, order them; then the whole year in a row: its peak and its record morning, its biggest rise, its falls, a mark across the year, and the swing read on the line graph the boxes become. Sixteen boards, recorded as they fall.

A new world for a new level: the Kestrel, a hot-air balloon, its altimeter logged every ten minutes. Watch Level 1's bars melt into a line, read a point, tap the top of the flight and every crossing of the ridge, reach the rise between two readings and turn it into a rate, find the steepest climb and the best twenty minutes, then load the pilot's minute log and see what the line only guessed. A fresh widget, Ascent. Checks on the 8:05 express.

The Kestrel's whole season: fifty-six flights and the top of each, a line that wobbles from one morning to the next while the summer lifts it. Read the direction over the season, tap the biggest jump, widen a window until the wobbles cancel and the turn still shows, reach the season's rise on the weekly line, find the trend's steepest step against the storm's leap, the turn, the mark, then cut the axis and read the rise off the labels. A fresh widget, Drift. Checks on Ines's training month.

Two seasons on one gauge: the Kestrel's weekly tops from the last lesson and the Heron's beside them. Which balloon flew higher, and whose tops rose faster: level is not pace. Reach the gap at week 7, tap the week the Kestrel first flew higher and every week it led, type how much more it rose, find the step where it gained most, then see the Heron drawn on its own gauge look the steeper and watch the two gauges slide into one. A fresh widget, Tandem. Checks on two cyclists' months.

One world, every figure of the level, one submission each. An apiary: the Amber hive's morning as a line, read at a point, over its best twenty minutes, across a mark and between two counts where the line only guesses; its spring of fifty-six mornings, the direction under the wobbles, the trend's steepest step against the leap after the rain, the window that keeps the turn, a mark across the weeks and the rise read off a cut gauge; then the Slate hive beside it on one gauge: who had more out and whose count grew faster, the gain, two gauges against one, the warmth crushed flat, and where the two moved apart. Fifteen boards, one submission each, a miss recorded and moved past.

Two numbers a boat: the Whitsun regatta's twenty-four boats, each a point at her sail area and her speed. Read a point both ways, find a boat from her two numbers, then read the whole cloud: its direction is the relationship, rises together, falls together, or none; the exception that breaks it; a corner of the cloud counted; one number guessed from the other; the cut frame that steepens a link and the gauge from zero that tells the truth; which figure answers whether two things go together. Checks on sixteen runners: hours against times, and why a relationship is not a cause.

The line through the fleet: a ruler settles through the regatta's cloud until as many boats stand above it as below, and reads the fleet's typical speed at any sail. Lay the line by hand with two buoys; read it where no boat stands; find every boat that beat her line by half a knot, and the one furthest under hers; measure a rope in numbers; tell a tight cloud from a loose one; count a fleet that stands in two groups and read the direction inside one; then the line run past the last boat, struck by a late entry. Checks at the harbour mouth: wind against swell, the line laid, read, and doubted beyond the windiest day.

The harbour register on one gauge, from a dinghy to a tanker: on the gauge from zero the fleet is crushed to a point, so the gauge stretches until every tick is a times-ten and every vessel stands at her own place. Read a vessel between two ticks; tap the one ten times another; count the vessels over a thousand tonnes; count the tens between two; see that equal gaps are equal ratios and never equal differences; place a vessel by hand with a buoy; find the middle of a gap; then the gauge slides back to zero and a finger apart turns out to be 240,000 tonnes; choose the gauge for the question. Checks on the beach at Fennick: a stone placed, the tens from a grain to a boulder, the gauge that holds them both.

The harbour register on two log gauges, length across and tonnes up: from zero the fleet is jammed into a corner, so both gauges stretch at once and the corner opens into a straight cloud, which is a rule. Tap the vessel ten times another's length and count the times up her tonnes; find every vessel over two ticks; read the rule off the slope (double the length, eight times the tonnes); place a vessel by buoy on both gauges; read the line where no vessel stands; find the vessel heaviest for her length by her rope; then the tonnes gauge slides back to zero and the rope changes its crown; choose the chart for the question; use the rule the other way. Checks on the beach at Fennick: the cobble's mass from the pebble's, a stone twice the pebble, the stone placed.

One world, every figure of the level, one submission each. The Solway: twenty oyster boats, each with her crew and her catch, and the harbour register, a dinghy to a tanker. The fleet as a cloud: a point read as two numbers, the direction, the exception that is not the direction, a corner read with both edges; the line laid by hand and read where no boat stands, the ray that is a rate, who is wrong when a boat sits under her line, and the line beyond the last boat. Then the register: the count of tens on the log gauge, the times hidden by the gauge from zero, the finger struck in tonnes, the gauges set by hand, the rule off the slope, and the extra tonnes that crown a different vessel than the times. Fifteen boards, one submission each, a miss recorded and moved past.

The Ashby market ledger, twenty-four stalls and five things each: the takings stand as the last levels' bars until the bars lie down into rows, every value exact, four more columns beside them. Read a cell; find the biggest on an unsorted table; sort by takings and take the fourth; count the rows over a mark; sort five stalls by hand; sort by since and mind the direction; read a rank; then the takings grow into bars and the split the table hid shows itself; choose the figure for the exact value; read back which column sorted a table. Checks on the Fennick allotments: a cell, four plots sorted by hand, the sort read back.

Filtering with Logic: a condition on a column keeps the rows it is true of; AND narrows, OR widens, NOT keeps everything but; a fresh widget, Sieve.

Filters with Inequalities: over, under, or more, or less; the threshold as a handle; a band; the boundary decides; a fresh widget, Sluice.

Grouping Data: one card per value of a column, one number each: the count, the total, the average; the question chooses the column; a fresh widget, Bundle.

Grouping and Filtering: a filter upstream of a grouping, one number per group for a subset; the order matters; a value with no survivor has no card; a fresh widget, Funnel.

Drawing Conclusions: a claim is checked against the cards of a named rig; the rig decides; a number rests on a count of rows; together is not a cause; a fresh widget, Verdict.

Transforming Data: a new column from old ones by a formula: a rate, an age, a share; sorted by it the ledger tells a new story; a fresh widget, Forge.

Counting Cafes: one question carried through the level's five instruments on a new world, the three markets: the rows that pass, the cards, the filter upstream, the claim on a rig, the column forged; every board one submission.

Best Bike Type: the Cycle Hire Case Study opens; one question, which type to buy more of, through the count, the total and the average, a claim on a rig, the conclusion that survives the switch, and the type cards handed to a bar chart and read.

Rate Recommendation: what a new e-bike should cost a day, read off the fleet's cloud: rate across, revenue up; the line laid and read where no bike stands, the exception, past the last bike a guess, cause or company, and the line no promise.

Best Quarter: where the next bike should stand, through a filter upstream of the quarter cards: the subset's number, the empty card, the filter's signature, the rig from words, the rig deciding, the conclusion that survives the switch, and the quarter cards handed to bars.