Following are the dot plots of heights of boys (in blue) and girls (in orange) of Grades 6, 7 and 8 (in that order) of two different schools. What do you notice? Share your observations. [School A means — Grade 6 boys 134.8, girls 137.78; Grade 7 boys 141.8, girls 141.83; Grade 8 boys 149.35, girls

Question

Accepted Answer

Set the twelve means out in one table and the story becomes clear.

Grade	School A boys	School A girls	School B boys	School B girls	B − A (boys)
Grade 6	134.80	137.78	149.84	150.20	+15.0 cm
Grade 7	141.80	141.83	156.14	155.41	+14.3 cm
Grade 8	149.35	147.81	156.14	156.83	+6.8 cm

1. The gap between the schools is huge. School B's Grade 6 students average about 150 cm — taller than School A's Grade 8 students. A Grade 6 child in School B is on average 15 cm taller than a Grade 6 child in School A. That is far bigger than any boy–girl difference anywhere in the data.

2. Heights rise with grade in both schools, but differently. School A gains about 7 cm from Grade 6 to Grade 7 and another 7.5 cm from Grade 7 to Grade 8. School B gains about 6 cm from Grade 6 to Grade 7 and then almost nothing from Grade 7 to Grade 8 — its boys' mean is 156.14 in both grades. School B's students seem to have finished most of their growing earlier.

3. Boys versus girls is not settled.

School A: girls slightly taller in Grade 6 (+3.0 cm) and Grade 7 (+0.03 cm — no real difference at all); boys taller in Grade 8 (+1.5 cm).
School B: girls slightly taller in Grade 6 (+0.4 cm) and Grade 8 (+0.7 cm); boys slightly taller in Grade 7 (+0.7 cm).

Five of these six differences are under 1.5 cm — smaller than the spread inside any single dot plot.

4. The dot plots show more than the means. In every plot the dots spread over 20 cm or more, so plenty of individual girls are taller than plenty of individual boys in the same grade, whichever mean is higher.

Why the schools might differ so much: the graphs cannot tell us. It could be nutrition, the age at which children start school, the region the schools are in, or simply which families send children there. The data raises the question; it does not answer it.

The strongest thing you can say: "In these two schools, boys and girls of the same grade are about equally tall, and the difference between the two schools is far larger than any difference between boys and girls." Data from two schools cannot settle whether boys are taller than girls in general — a question about a whole country needs data from a whole country.

NCERT Solutions for Class 7th Maths Chapter 5 Math Talk — Data Detective