Calculations with the Mean Flashcards

All 4 cards in this deck

What are the steps to find the mean of the remaining values when two means are known?

e.g. the mean of 8 parcels is $2.5$ kg; the mean of 3 of them is $2$ kg — find the mean of the other 5

1. Total of all: $8 \times 2.5 = 20$
2. Total of the known group: $3 \times 2 = 6$
3. $(20 - 6) \div 5 = 2.8$ kg

What are the steps to find the mean of two groups combined?

e.g. 18 boys with mean age $16.2$ years and 27 girls with mean age $16.7$ years

1. Total for each group: $18 \times 16.2 = 291.6$ and $27 \times 16.7 = 450.9$
2. Add the totals: $742.5$
3. Divide by the total frequency: $742.5 \div 45 = 16.5$ years

True or false? The mean of two groups combined is the mean of the two group means.

False. You must use the group totals; averaging the two means only works if the groups are the same size.

True or false? If one value in a data set is replaced by a larger value, the mean increases.

True. The total increases while the number of values stays the same.