> ## Content Index > Fetch the complete content index at: https://www.esheets.io/llms.txt > Use this file to discover other available public pages before exploring further. # Combined Means - URL: https://www.esheets.io/combined-means/ - Published: 2026-10-01T18:07:51.000Z - Updated: 2026-10-01T18:07:51.000Z - Author: Richard Linnington - Tags: Maths, Statistics Practise calculating combined means when groups have different sizes. These eight GCSE questions cover weighted means, an extra result that changes a mean, and finding a missing group mean from an overall average. Work with everyday contexts, decimal values and a ratio of group sizes. A calculator can help with the arithmetic while you focus on choosing the correct totals and number of values. [Jump to the questions](#practise-now) ## Practise now Worksheet preview and key skills ### Worksheet preview Eight calculator-friendly questions progress from combining two groups to finding an unknown mean in four groups. Each question has one numeric answer. You will use exact whole numbers and decimals, with no rounding required. New questions provide fresh numbers to practise the same skills. #### What you’ll practise - Reconstructing totals using number × mean and combining two or three groups. - Finding missing group means and a new result when the mean changes. - Using a ratio to find group sizes before working backwards from an overall mean. Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked example. ## Combined Means Calculate each missing mean or result. You may use a calculator; enter an exact whole number or decimal without units (no rounding or fractions). ## Topic guide ### What is a combined mean? A combined mean is the mean of all the values in two or more groups. A larger group contributes more values, so its mean has more weight. You need to know each group’s size as well as its mean. ### Use totals first 1. Work out each group’s total: total = number × mean. 2. Add the totals to combine groups, or subtract known totals from the overall total to find a missing total. 3. Divide by the relevant number of values: all values for a combined mean, or the missing group’s size for its mean. ### Worked example: combining groups Eight orders have a mean price of £12 and twelve other orders have a mean price of £17\. The totals are 8 × £12 = £96 and 12 × £17 = £204\. There are 20 orders altogether, so the combined mean is (£96 + £204) ÷ 20 = **£15**. ### Worked example: finding a missing mean A club has 30 members with an overall mean age of 24 years. Ten members have a mean age of 18 years. Find the mean age of the other 20 members. The overall total of the ages is 30 × 24 = 720 years. The known group’s total is 10 × 18 = 180 years. Subtract totals: 720 − 180 = 540 years. The missing mean is 540 ÷ 20 = **27 years**. ### One extra result and ratios If a mean changes after one extra result, subtract the old total from the new total. For example, five games with a mean score of 14 give a total of 70\. Six games with a mean of 16 give a total of 96, so the sixth score is 96 − 70 = **26**. For a ratio, find the group sizes first. If 35 people are split in the ratio 2:5, one part is 35 ÷ 7 = 5 people, giving groups of 10 and 25\. Then use their sizes to reconstruct totals. With several groups, subtract every known group total from the overall total before dividing by the missing group’s size. ### Common mistakes to avoid - Do not simply average two group means unless the groups are the same size. - Multiply each mean by its group size before combining information. - Divide by the correct number of values, not the number of groups. - In reverse problems, subtract totals, not means. - Keep intermediate values exact. This worksheet needs no rounding; enter whole numbers or decimals without units. Check that a combined mean lies between the smallest and largest group means. It should be closer to the mean of a larger group when combining two unequal groups.