One number for a group

The idea

A single number can represent a group of values; the total is one such number, but it may not be appropriate for comparing groups of different sizes.

Who played better?

Shubman scored 110 runs in 5 matches. Yashasvi scored 96 runs in 4 matches. Vaishnavi says, “Shubman performed better. His total is bigger.”

What do you think of Vaishnavi’s statement?

• She is right: 110 is more than 96
• Not fair: they played different numbers of matches
• Totals can never be used

Change the size of the group

Each member of a group makes the same amount. Add or remove members and watch the totals.

The total follows the size

You made a total bigger without anyone doing better. You only added members. A group of 5 matches has more chances to add runs than a group of 4 matches.

A single number can stand for a whole group of values. The total is one such number. But if the groups have different sizes, the total is not a fair way to compare them.

A single number can represent a group of values. The total is one such number, but it may not be appropriate for comparing groups of different sizes.

• Player | Matches | Total runs
• Shubman | 5 | 110
• Yashasvi | 4 | 96

Notes

A single number can represent a group of values. The total is one such number, but it may not be appropriate for comparing groups of different sizes.

Check yourself

Class 7A (30 students) collected 150 bottles and class 7B (20 students) collected 120 bottles. Ria says, “7A did better. Its total is bigger.” What do you think?

When is it fair to compare two groups by their totals?

Every Red player scores 5 runs. How many Red players give a total of 35 runs?

Answer: 7

35 ÷ 5 = 7 players, since 7 × 5 = 35.

Shubman has 110 runs in 5 matches and Yashasvi has 96 runs in 4 matches. Which important fact does the comparison of totals leave out?

• She is right. The bigger total always means the better group.. A bigger group gets a bigger total just by having more members.
• The total alone cannot say, because 7A has more students. — correct. Yes! A group with more members can have the bigger total even if each member collects less.
• She is wrong. The smaller total is always the better one.. Totals do not work like that either. The sizes of the groups must be taken into account.
• When both totals are big numbers. Big numbers do not help. The sizes of the groups matter.
• When one group has many more members. That is exactly when the total is unfair.
• When both groups have the same number of members — correct. Yes! With equal sizes, a bigger total comes from the members, not from the count.
• Yashasvi’s total is smaller.. We already see that from the totals. The totals do not show the number of matches.
• Both are cricketers.. That is true but does not help to compare them.
• Shubman played one more match than Yashasvi. — correct. Yes! One more match gives more runs to add up. The totals hide this.