5. Tales by Dots and Lines

Part II, printed Chapter 59 topics1 h

Chapter 5 of NCERT Mathematics for Class 8 (Part II, printed Chapter 5): Tales by Dots and Lines. Three sections — The mean as a balance point, Median, and computing with real data and Reading and making data graphics. Nine videos, 1 h in all.

Worked answers to the 29 exercise questions in this chapter →

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Part 1

The mean as a balance point

10 minThe mean as the point where the distances balanceDividing the total by the count looks like a recipe for sharing. It is also, silently, an instruction about a position on the number line.10 min · 12 parts10 minWhich added values move the mean, and in which directionOne sentence answers this whole topic. A new value drags the average towards itself and never past itself.10 min · 12 parts

Part 2

Median, and computing with real data

9 minWhether adding a value raises or lowers the medianThe median only ever asks a value which side it is on. Never how far away it is.9 min · 12 parts10 minWorking backwards from an average to a missing valueAn average is not a summary that has forgotten the numbers. It is a record of their total, which is why it can be run backwards.10 min · 12 parts9 minMean and median from a frequency table, by hand and in a spreadsheetA frequency table is an ordinary list with the repetitions folded up. Every rule for computing with one falls out of unfolding it.9 min · 12 parts

Part 3

Reading and making data graphics

10 minLine graphs, and what change over time looks likeDrawing the same twelve numbers as a line instead of columns adds no figure at all to the data. It adds a claim.10 min · 12 parts11 minInterrogating a real dataset: traffic, and rainfallA graph is evidence for some claims and silent about others. The whole skill is telling those apart before you speak.11 min · 12 parts11 minInfographics and activity strips: what a visual shows and what it hidesAn encoding buys you a pattern and spends the numbers to buy it. The question is never whether it is accurate.11 min · 12 parts10 minTelling a story with data, and letting it raise the next questionA data story does not end in a conclusion. It ends in a better question — one that names the data it would need.10 min · 12 parts

What you will be able to do

  • Compute the mean of a small collection from its dot plot and mark it on the same axis
  • Predict, given the mean of a collection and one new value, whether the mean will rise, fall or stay put, before computing anything
  • State the median of a small collection, choosing correctly between the single middle value and the average of two
  • Convert a stated average and count into the total of the data
  • Explain what a frequency table records, and reconstruct the underlying list from one
  • State what a line graph adds to a column graph of the same data, and what it does not
  • State, for an unfamiliar figure, what its axes, units, interval, series and source are before interpreting anything
  • State what quantity an infographic's colours encode, and read a state's value from the scale
  • Describe the shape of a curve in words, naming where it falls, flattens and rises

What this chapter assumes you already know

  • Computing a mean as total ÷ count, and a median as the middle value of sorted data — both are recalled, not taught, at the head of this chapter
  • Reading a dot plot: one dot per value, stacked when a value repeats — carried in from earlier classes; this chapter uses dot plots from its first page without re-explaining them
  • Subtracting to find the distance between two points on a number line, with half-units
  • Adding a short list of decimals, and dividing a whole number by 3 or 4 to get a decimal answer
  • That a number line's tick labels may step by 2 while the drawn grid lets a dot sit on the odd values between them
  • Mean = total ÷ count, and the same equation read as total = mean × count
  • Reading and adding values off a dot plot, including stacked dots and half-units
  • Writing a general collection as x₁, x₂, … xₙ, and knowing that n stands for how many there are

It builds directly on What happens to a product when you nudge one factor and Building a pie chart: turning counts into angles.

Where people usually slip up

Sentences students actually say, taken from the notes the videos were made from. Each one is answered on the page of the video it belongs to.

  • "The mean is halfway between the smallest and the largest."
  • "The mean has to be one of the values."
  • "Balance means the same number of values on each side."
  • "Distances left and right — so the mean is where the arrows are longest."
  • "If I move the centre a little, the two sides stay nearly balanced, so any nearby point works too."
  • "The mean tells me what the collection looks like."
  • "More values means a bigger average."
  • "The mean moves to the new value."