Maths Made Easy Forums Standard Data & Statistics Worded Average Problems

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Keymaster
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Isabella has completed four assessment tasks, each marked out of 100, giving her a mean of 71%. She wants to increase her mean to 75% after the trial. Which of the following below will calculate the mark (x) she needs to achieve in the next assessment task?
a. $$x=\frac{71+75}{2}$$

b. $$x=\frac{71+75}{2}$$

c. $$75=\frac{71\times4+x}{2}$$

d. $$75=\frac{71\times4+x}{5}$$

the total of 4 tests with an average of 71 will be 71 × 4
then the 5th test is x
so the total of all five tests will be 71 × 4 + x

to find the average of these 5 tests, divide by 5

since the average is to be 75 then $$75=\frac{71\times4+x}{5}$$
D

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Keymaster
Post count: 718
 The mean height of the 5 Sydney storm basketball players on the court at the start of a game was 1.90m. During the game, a player who is 1.85m tall was injured and was replaced by a player who is 1.95m tall. What was the mean height of the 5 players after the replacement? 5 × 1.9 = 9.5m first we find the total of the 5 players: If they have a mean of 1.9, then the total heights would be 5 lots of 1.9 9.5 – 1.85 = 7.65 remove the 1.85 player 7.65 + 1.95 = 9.6 now add in the replacement player at 1.95 9.6 ÷ 5 = 1.92 to find the new mean, divide the new total by 5, since there are still only 5 players on the court ∴ mean = 1.92m

Keymaster
Post count: 718
 The average temperature in June for the past 30 years in a city has been 65.2. This year the average June temperature was 71.5. What is the new 31 year average? 65.2 × 30 find the total for the last 30 years if the average was 65.2, that means that each year can be considered as 65.2 and since there were 30 years, to find the total you multiply 65.2 by 30 =1956 the total for the 30 years is 1956 1956 + 71.5 = 2027.5 to find the new total for the 31 years, add the 30 year total to the new temperature 2027.5 ÷ 31 = 65.4 to find the new average for the 31 years, divide the new total by 31