Dot plots: seeing spread and clustering at a glance

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What the video covers, what to say before it, where a class usually goes wrong, and what to set afterwards. An account is free, and it opens every chapter of every book.

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What to assume they know

The arithmetic mean as fair-share — the mean as a total shared out equally
Reading a number line with equal spacing, and locating a whole number on it
Class 6 Ganita Prakash: making a tally and drawing a bar graph from it
Comparing two two-digit numbers, and finding the largest and smallest in a list
Subtraction of two-digit numbers (for the gap between the extremes)

What they should be able to do

Build a dot plot from a list of values: one dot per value, stacked where a value repeats
Read a value's number of occurrences off the height of its stack
Explain why the chapter's price line starts at 10 rather than at 0, and what that costs
Describe a data set from its plot using the words the chapter uses — clustered, spread out, minimum, maximum
Say which questions a dot plot can answer and which the original table is still needed for
Compare two data sets by putting their dot plots on the same scale
Mark a mean and a median onto a dot plot, and read off which side of the cluster each of them falls

Where it usually goes wrong

"The height of a stack is a quantity." It is a count. In the onion plot the two-dot stack at 42 does not mean ₹84; it means two months cost ₹42. This is the commonest first error with a dot plot and it should be named out loud.
"A dot plot is a bar graph made of dots." A bar graph puts a category on one line and a size on the other. A dot plot puts the values themselves on the line and counts them upwards. The onion data is drawn both ways in this chapter — as a dot plot on p.103 and as a clustered column graph on p.115 — which makes the difference easy to show.
"A line that does not start at zero is a mistake." The chapter starts at 10 on purpose and says why. The honest point is narrower: it is a choice, it must be visible, and it changes how big the differences look. The same issue comes back with a vertical line beginning at 145 cm in §5.4, so set it up here.
"Sorting the data loses nothing." It loses the sequence, and the chapter makes that explicit by asking for January's price — a question the plot can no longer answer. Keep both displays in view together when you say this.
"More spread means a bigger average." Independent things. Wahapur's prices are the more spread out and its total is the smaller of the two.
"Every dot is a different thing." Two dots at the same value are two months with the same price, not one month counted twice — and the chapter's callout at 39 makes the harder version of the point: the same value can belong to two different towns.

Questions to check understanding

Draw a dot plot from a given list of values
Read a dot plot back into a list, or read off how many values a plot holds
State the minimum, the maximum and the gap between them from a plot
Compare two dot plots on a shared scale and describe which set is the more spread out
"Which of these statements is true of these two dot plots?" — the chapter's own format at Part II, §5.4, p.129, where four statements about pockets on clothing have to be judged from two plots alone
Say what a plot cannot tell you, given the table it came from
Mark a stated mean and median onto a plot and describe which side of the cluster each lands

Examples worth working on the board

The onion price table (Part II, §5.2, pp.101–102). Checked against p.102. Monthly price in rupees per kilogram, January to December. Yahapur: 25, 24, 26, 28, 30, 35, 39, 43, 49, 56, 59, 44. Wahapur: 19, 17, 23, 30, 38, 35, 42, 39, 53, 60, 52, 42. This one table carries three topics of this chapter.
The five students' comparisons (Part II, §5.2, p.102). In paraphrase: one picks Wahapur because it holds the single highest price; one adds each column and reports 458 against 450; one counts how many Wahapur prices sit in the fifties; one goes month by month and reports that Yahapur is dearer in six months, Wahapur in five, and that one month ties; one reports the gap between each town's highest and lowest price, 59 − 24 for Yahapur and 60 − 17 for Wahapur. Note: the third of these, the count of high prices, is the one whose stated number.
The dot plot itself (Part II, §5.2, p.103). Checked against p.103. Two plots, one above the other, on identical lines running from 10 to 60. Yahapur's values are green circles, Wahapur's are purple diamonds. Three callout boxes are printed beside them: one points at 39, which occurs once in each town; one at 19, a Wahapur value; one at 42, which occurs twice and both times in Wahapur, so it is drawn as a stack of two. Rebuild the plot rather than lifting it, but keep the two-dot stack — a repeat is what the vertical direction is for.
The starting value (Part II, §5.2, p.103). Input: the line begins at 10, not 0, and the chapter gives its reason — no value falls below 10 or above 60.
The two questions the chapter asks about the plot (Part II, §5.2, p.103). In paraphrase: does the picture hold everything the tables held, and can you read January's Yahapur price off it? The chapter answers both in the paragraph immediately below them — the plot sorts the values and loses the month-wise sequence, so January cannot be recovered from it. What stays unanswered anywhere in this file is the "Figure it Out" and "Math Talk" material; there is no answer key.
Family-height plots with mean and median marked (Part II, §5.2, p.106). Checked against the printed page. Two pairs of plots on a shared 115–175 line — the upper pair carries the means only, the lower pair repeats the same two data sets with the medians added. Within each pair the upper plot is Yaangba's family, 155, 160, 164, 165, 169, 173, drawn in yellow diamonds, and the lower is Poovizhi's, 118, 165, 170, 173, 175, drawn in blue circles. The mean is a solid vertical rule and the median a dashed one, with their values printed at the right-hand end. The two-stage reveal is the point of the figure, so keep it as two stages; and use the same two line styles across every plot in the explanation.
Class 5 class-height plots (Part II, §5.2, p.109). Checked against the printed page. Three plots on a shared line whose labels run from 125 to 155; the line itself runs on past 155, far enough to carry the 156 and the 158. Boys: 147, 135, 130, 154, 128, 135, 134, 158, 155, 146, 146, 142, 140, 141, 144, 145, 150. Girls: 143, 136, 150, 144, 154, 140, 145, 148, 156, 150, 150. The whole class is the two lists together.
Estimating a minute (Part II, §5.2, p.110). Checked against the printed page. Two dot plots on a shared line from 40 to 70 seconds, one per group of children, with each group's mean and median printed beside it: Group A, mean 58.21 and median 60; Group B, mean 59.28 and median 59.5. The underlying seconds are drawn, not printed, so treat the shapes as the input: Group A runs further to the left and has a long thin low tail; Group B is packed more tightly around the middle with a tall stack near 59–60. Do not state either group's number of children — the dots are artwork and a miscount would be invented data.
Empty plots for the reader to fill (Part II, §5.2, pp.107, 108, 112–113). Checked against pp.107, 108, 112 and 113. Four blank grids with only the line numbered: 0–40 for short stories read, 0–25 for newspaper pages (the grid runs on a little past 25, so the 26 still fits), 0–80 for date-palm heights, 0–4.5 for newborn weights. Three of the four data sets are typeset and can be given straight to the explanation — only the fifteen bookworm slips on p.107 are artwork. The newborn weights are a printed table at the head of Part II p.113 (six boys' figures and six girls'), verified on the printed page and present in the extraction. The other two: newspaper pages 16, 18, 20, 22, 26, 16, 10, and palm heights 50, 45, 43, 52, 61, 63, 46, 55, 60, 55, 59, 56, 56, 49, 54, 65, 66, 51, 44, 58, 60, 54, 52, 57, 61, 62, 60, 60, 67.

Figures to have open

A dot plot builder: an empty number line that accepts values one at a time and stacks repeats. Standard schematic, but it must be the same object reused in sections 4, 10, 11 and 12 — an added argument is that one picture serves many data sets.
The two onion dot plots on a shared 10–60 line, in two distinguishable colours and two distinguishable marker shapes. Redraw; the book's own uses green circles and purple diamonds for exactly this reason and the shape difference must survive greyscale.
The price table and the dot plot side by side, so that "which month?" can be shown answerable on one and not the other.
Mean and median rules in two line styles, solid and dashed, matching the book's convention on pp.106 and 109.
No figure needs to be taken from the textbook.

Where this sits in the book

NCERT Ganita Prakash, Class 7, Part II, printed Chapter 5, "Connecting the Dots...", §5.2 "Representative Values", pp.101–104 for the dot plot's introduction, and pp.106–113 for its later uses. The named sub-headings used are "Know Your Onions!" (pp.101–102), "Outliers and Medians" (pp.105–109), "Of Ends and the Essence" (pp.109–112) and the second "Figure it Out" (pp.112–113). None carries a number.
The SUMMARY's one-line account of what a dot plot is for: Part II, p.134.
The pockets-on-clothing plots used as an assessment model: Part II, §5.4, p.129.
Source file gegp205.pdf / gegp205.txt, printed pp.97–135; PDF page 1 is printed page 97.