Read data before calculating

In this new table, A–D are consecutive periods and the two series record separate production lines. For a question about A and B, leave C and D out. Series 1 totals 30 + 70 = 100 units; Series 2 totals 34 + 26 = 60 units.

For the combined total across A and B, add the subtotals: 100 + 60 = 160 units. For how many more units Series 1 produced, subtract: 100 − 60 = 40 units.

For Series 1’s share across A and B, divide its subtotal by the combined total: 100 ÷ 160 × 100 = 62.5%. The denominator includes both series in the requested periods.

For the percentage increase from A to B, first combine each period: A is 30 + 34 = 64 units; B is 70 + 26 = 96 units. Then (96 − 64) ÷ 64 × 100 = 50%. Divide the change by the earlier total. Averaging the two series’ percentage changes can give a different, incorrect result.

Missing entries

Recover a missing value from a total or average.

A = 12; B = 18; C = ?; D = 30

The total is 80. What is the missing value for C?

80 − (12 + 18 + 30) = 20.

The mean of all four values is 20. What is the missing value for C?

First recover the total: 20 × 4 = 80. Then subtract the known values: 80 − (12 + 18 + 30) = 20.

Weighted averages

Account for different group sizes.

Value: A = 10, B = 20, C = 30, D = 40. Group size: A = 1, B = 2, C = 3, D = 4.

What is the weighted mean for groups A, B, C, D? Use their group sizes as weights.

Weight each value, then divide by the combined group size: (10 × 1 + 20 × 2 + 30 × 3 + 40 × 4) ÷ (1 + 2 + 3 + 4) = 30.

A = 10; B = 20; C = ?; D = 40

The weighted mean of all four groups is 30. What is the missing value for C?

Weighted total: 30 × 10 = 300. Subtract the known weighted values, then divide by the missing group’s size: (300 − (10 × 1 + 20 × 2 + 40 × 4)) ÷ 3 = 30.

Rates and units

Combine data, then convert units or calculate a rate.

Litres: A = 20, B = 30.

Each container holds 5 litres. How many full containers can be filled using all the liquid from A, B?

Add the selected litres, then divide by litres per container: (20 + 30) ÷ 5 = 10.

Units produced: A = 20, B = 30.

Each period lasts 15 minutes. What is the average production rate per hour across A, B?

The selected periods last 30 minutes in total. (20 + 30) × 60 ÷ 30 = 100 units per hour.

Link two sources before calculating

One table gives sales quantities. The other gives prices and costs. Match each product by its label, even when the rows are in a different order.

Fictional data for one period. All money values use the same unit.

Find the combined revenue from A and B. Use only their quantities and prices. Unit costs and the other products are not needed.

A: 60 × 9 = 540; B: 40 × 12 = 480

540 + 480 = 1,020

Check: which product, A or B, has the larger profit, and by how much? Use profit = units sold × (price − cost). Work it out before opening the answer.

Use this new table. Find the percentage increase in the combined output of both series from A to C. B and D are not part of the calculation.

First add both series within each requested period. Subtract the earlier total from the later total, divide by the earlier total, and multiply by 100.