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# Mean, median and mode watch

1. The answer to this question is 19, how do you solve to get it?
'Joe scored these marks out of 20 in six maths tests.

11 9 5 13 15 12
How many marks must he score in the next test so that his mean mark and his median mark are the same?
2. How do you solve this question, the answer to it is 32?
Jacqui writes down the length, in cm, of plants on a piece of paper:
23, 29, 14, 23,17, 23
She accidentally rips off the last result. Jacqui states that the mean, the median and the mode are all equal. Work out the value of the missing number.
3. (Original post by BT144)
How do you solve this question, the answer to it is 32?
Jacqui writes down the length, in cm, of plants on a piece of paper:
23, 29, 14, 23,17, 23
She accidentally rips off the last result. Jacqui states that the mean, the median and the mode are all equal. Work out the value of the missing number.
The mode is the most often number so despite what the number she ripped off was the mode would still be 23. Therefore what number can be added so that the mean and median is also 23?
4. (Original post by BT144)
The answer to this question is 19, how do you solve to get it?
Let x be an additional number that is added to the list so that the list now reads:
5,9,11,12,13,15,x
Mean = Σ List ÷ 7 = (65+x)÷7
Median Value Location = (n+1)/2 = (7+1)/2 = 8/2 = 4
Hence Median Value is 12.
Let mean = median
(65+x)÷7 = 12
Multiply by 7:
65+x = 84
Minus 84:
x = 19
Hence, the extra value would have to be 19 for the mean and median to be equal.
5. I'm fairly sure you could do it with normal distribution too but I think that may be above the level required for this problem
6. (Original post by BT144)
The answer to this question is 19, how do you solve to get it?
'Joe scored these marks out of 20 in six maths tests.

11 9 5 13 15 12
How many marks must he score in the next test so that his mean mark and his median mark are the same?
First, let's write them in order to see what the median would be, along with x:

5 9 11 12 13 15 x

We see that the median is 12, so that must be the mean as well.

Now add all numbers and x together, and form an equation.

(5+9+11+12+13+15+x)/7 = 12 [simplify then multiply both sides by 7]

65 + x = 12*7 [subtract 65 from both sides to get your answer]

x = 84 - 65

x = 19

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