Class 7 Maths Part 2 Chapter 5: Connecting the Dots… Notes

What is this chapter about?

Your teacher is meeting two old friends, one 5 feet tall and one 6 feet tall, and you are asked to guess which is a man and which is a woman. You cannot be sure, but experience says tall women and short men are less common, so most people guess the same way. That is statistical thinking: using data to say what is likely, not what is certain. This chapter is about asking questions that data can answer, choosing one number to represent a group of numbers, and drawing data so that its story shows.

Statistical questions

A statistical question is one you answer by collecting data while expecting the answers to differ. “How tall are Grade 7 students in our school?” is statistical, because heights change from student to student. “What is 15 × 4?” is not; it has one fixed answer. Statistics is the subject of collecting data, organising and analysing it, and interpreting and presenting what it shows.

The mean: a fair share

In one series Shubman made 110 runs in 5 matches and Yashasvi made 96 runs in 4, so comparing totals is unfair. Divide each total by the number of matches: 110 ÷ 5 = 22 and 96 ÷ 4 = 24, so Yashasvi scored more per match. (The book prints 110 ÷ 5 = 21; the right value is 22, and the conclusion stays the same.) This arithmetic mean, or average, is the sum of the values divided by how many values there are. It is also a fair share: if Shreyas’s group of 5 pools 30 guavas and shares them equally, each gets 6. A 0 is a real value and counts, but a missing value, such as a match not played, is left out. Read more in mean and representative values.

The median and outliers

Poovizhi’s family heights are 170, 173, 165, 118 and 175 cm. Their mean, 160.2 cm, falls below four of the five heights, because the young child’s 118 cm drags it down. A value so far from the rest is an outlier. The median, the middle of the sorted values, is 170 cm and describes the family much better. With an even number of values, average the two middle ones to get the median. The mean and the median are called measures of central tendency, since they show where the values pile up. See median and outliers.

Dot plots and spread

A dot plot puts one dot for each value above a number line. It loses the original order, so you cannot read January’s onion price from it, but it shows at a glance the smallest value, the largest value and where the values crowd together. On the onion dot plots, Wahapur’s prices, from ₹17 to ₹60, spread wider than Yahapur’s, from ₹24 to ₹59.

Clustered bar graphs

To compare two groups one category at a time, draw their bars next to each other: a clustered bar graph, also called a double bar graph when each cluster has two bars. Colours with a key tell the groups apart, and dots or slanted lines inside the bars help readers who cannot tell the colours apart. A graph can hold a lot, so read it in two steps: first identify what is given (how it is organised, the scale, the patterns), then infer what it means and test which claims the data supports. Read visualising data.

Data detective

The chapter closes with a table of the average heights of Indian boys and girls aged 5 to 19 in 1989, 1999, 2009 and 2019. Read closely, it shows children of every age taller in 2019 than in 1989, girls a little taller than boys at ages 11 and 12 in every survey, and boys pulling ahead from 13 onwards. Good data tells a story and raises new questions too. Answers to every question, including the number lock puzzle, are in the NCERT solutions for Part 2 Chapter 5.