5. Connecting the Dots...

8 topics1 h

Chapter 5 of NCERT Mathematics for Class 7: Connecting the Dots.... Four sections — Asking a question data can answer, Representative values and variability, Visualising data and Reading data critically. Eight videos, 1 h in all.

Worked answers to the 29 exercise questions in this chapter →

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Part 1

Asking a question data can answer

10 minTurning a vague comparison into a question with a data answerTwo friends are coming round: one five feet, one six; one a woman, one a man. Which is which? You have an answer, and it is a guess.10 min · 12 partsहिंदी

Part 2

Representative values and variability

9 minThe arithmetic mean as fair-shareTwo batters, four matches each, four different summaries — and four different verdicts about who is better.9 min · 12 partsहिंदी9 minDot plots: seeing spread and clustering at a glanceTwo towns, twelve months, twenty-four onion prices, one question: which town is dearer? Five people answer five different ways.9 min · 12 partsहिंदी10 minOutliers, and why the median survives themTwo families, eleven people, every height measured. The average says the second family is shorter. Then go and look at them.10 min · 12 partsहिंदी9 minWhy one number is never enough to describe a data set“How tall is your class?” has no one-number answer, and not because the question is sloppy. Every summary is a deliberate loss.9 min · 12 partsहिंदी

Part 3

Visualising data

10 minClustered bar graphs: comparing across categories and across timeA year of onion prices in two towns, drawn as two graphs on identical scales. Nothing is wrong with either one.10 min · 12 partsहिंदी

Part 4

Reading data critically

11 minTelling tall tales: how a truthful graph still misleadsA family measures everybody, takes the average height, and builds a doorway exactly that tall. How many of them have to stoop?11 min · 13 partsहिंदी9 minWhy every answer from data raises the next questionOnions cost thirty-five a kilo. Any questions? Now here is a year of prices in two towns, and suddenly there are six.9 min · 13 partsहिंदी

What you will be able to do

  • Distinguish a statistical question from one that a single look-up answers
  • State why the total of a group is not a fair basis for comparing two groups of different sizes
  • Build a dot plot from a list of values: one dot per value, stacked where a value repeats
  • Find the median of a sorted list, for an odd and for an even number of values
  • State the four things a data set can be described by, in the chapter's own list: the ends, the total, the gap between the ends, and the two measures of central tendency
  • Read a value off a clustered column graph by referring to the markings on the vertical line
  • Judge whether a stated claim is supported by a given table or graph, and give the reason either way
  • Explain why variation in data provokes curiosity and a single flat figure does not

What this chapter assumes you already know

  • Reading a small two-row table of numbers
  • Class 6 Ganita Prakash: collecting and tallying data, and drawing a simple bar graph from it
  • Knowing that a rupees-per-kilogram price can change from month to month
  • Being able to say what would have to be measured to test a claim
  • Division with a remainder, and division giving a decimal answer
  • Reading a small table with a blank cell in it
  • Class 6 Ganita Prakash: adding a short list of whole numbers reliably
  • Reading a number line with equal spacing, and locating a whole number on it

It builds directly on When an approximate answer is the better answer.

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.

  • "A statistical question is any question with a number for an answer."
  • "If the answer varies, the question is badly asked."
  • "'Men are taller than women' means every man is taller than every woman."
  • "Statistics means calculating averages."
  • "A question about a single person can't be statistical."
  • "Collecting data settles the question for good."
  • "The bigger total wins."
  • "The average is always one of the numbers you started with."