NCERT Class 7 Ganita Prakash 2 Chapter 05 Connecting the Dots PDF Download

Chapter 5: Connecting the Dots...

5.1 Of Questions and Statements

Your teacher tells you that they are meeting two of their childhood friends this evening. One is 5 feet tall and the other is 6 feet tall. What is your guess as to each friend's gender based on this information?

You might have guessed that the 5-foot-tall person is a woman and the 6-foot-tall person is a man. There is a chance that you are wrong. But experience tells us that 5-foot-tall men and 6-foot-tall women are rare. We have seen that, more often, men are taller than women.

The above is a simple example of statistical thinking. We regularly come across statements like:

• Jemimah's batting has been very consistent over the past year. We can expect a century from her in tomorrow's match.
• I take about 15 minutes to cycle from school to home.
• I think my pen might last for 2 more weeks; it is time to get a new one soon.
• The population of their village has reduced by about 100 in the last decade.
• Since I started to eat fruits and vegetables more frequently, I am able to run 2 km more each day.
• David spends about 7 hours daily in the school.

We call these statistical statements. Simply put, a statistical statement is a claim or summary about some phenomenon, expressed in terms of numerical values, proportions, probabilities, or predictions.

A statistical question is a question that can be answered by collecting data. For example, "How tall are Grade 7 students in our school?" is a statistical question. We expect that not all Grade 7 students have the same height, but we can collect data, analyse it, and make conclusions about the heights that do occur. The question "Typically, are onions costlier in Yahapur or Wahapur?" is also a statistical question. Prices can vary over time. Therefore, answering this question requires us to look at data, analyse it, and come to conclusions making suitable statistical statements.

Which of the following are statistical questions?

1. What is the price of a tennis ball in India?
2. How old are the dogs that live on this street?
3. What fraction of the students in your class like walking up a hill?
4. Do you like reading?
5. Approximately how many bricks are in this wall?
6. Who was the best bowler in the match yesterday?
7. What was the rainfall pattern in Barmer last year?

The term statistics refers to the study of collecting, organising, analysing, interpreting, and presenting data. In this chapter, we shall encounter some statistical questions and learn how analysing data and graphs can help answer them.

Teacher's Note

A statistical question must allow for variation in answers. "Do you like reading?" is not statistical because it has a fixed yes-or-no answer for each person. But "What fraction of students in your class like walking up a hill?" is statistical because you need to collect data from many students and then analyse it. When you see a question in an exam, check: does answering it require collecting and analysing data, or is it just asking for a single fact?

5.2 Representative Values

The runs scored by Shubman and Yashasvi in a cricket series are given in the table below. Who do you think performed better?

Shreyas says, "Both their performances are similar since Yashasvi scored more in the first and second matches, whereas Shubman scored more in the third and fourth".

Vaishnavi says, "I think Shubman performed better because he scored the highest number of run in a match - 90!".

Shreyas says, "No! Yashasvi batted better since the total number of runs he made is 175, while Shubman made only 128".

Vaishnavi says, "Oh! Also, Yashasvi's batting is more consistent - the difference between his maximum score and minimum score is lower".

The table below shows the runs scored by these two players in another series. Who do you think performed better in this series?

Vaishnavi says, "Here, Shubman performed better since his total is 110 runs, while Yashasvi's total is 96 runs".

What do you think of Vaishnavi's statement?

Shreyas says, "But Yashasvi made 96 runs in 4 matches and Shubman made 110 runs in 5 matches".

So, how do we say who performed better? It is often not simple to compare two groups of numbers and clearly say that one is better than the other.

Can a single number act as a representative of a group of numbers? For example, can we represent Shubman's or Yashasvi's batting in this series with one number? Discuss.

We saw one way already - the total of the values in the group! But, if the group sizes are different, then the total may not be an appropriate measure to compare.

In some matches, a player could have scored more and in other matches less. A representative number for the group can be found by balancing out these highs and lows. For example, we can add up the runs scored in all the matches and divide the total by the number of matches played. We call this value the average or arithmetic mean of the given data.

Here, the average number of runs scored by a player in a match = [Total runs scored by the player in all the matches] \( \div \) [Number of matches played].

Average number of runs scored by Shubman in a match = 110 \( \div \) 5 = 21 runs.

Average number of runs scored by Yashasvi in a match = 96 \( \div \) 4 = 24 runs.

In this series, Yashasvi's average number of runs is higher than Shubman's.

Teacher's Note

When comparing two data sets of different sizes, always use the average (or another representative value), not just the total. Vaishnavi's mistake was comparing 110 runs to 96 runs without noticing they came from different numbers of matches. Divide the total by the count first, and then compare the averages fairly.

Key Points

• A statistical question is one that requires collecting and analysing data to answer, not a question with a single fixed answer. Questions that expect variation in responses across a group are statistical.
• A statistical statement is a claim or summary about data expressed using numbers, proportions, probabilities, or predictions based on observed patterns.
• When comparing two groups of different sizes, use the average (arithmetic mean) rather than the total. The average is found by dividing the sum of all values by the number of values.
• The average is a representative value that balances out the highs and lows in a group of numbers, making it useful for fair comparison.

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