The mode, the mean and the median
The mode, the mean and the median
The mode is the value that comes up the most times – the value with the largest frequency.
- For 6B’s pets the mode is dog: 9 pupils chose it.
- The shoe sizes of 10 pupils: 36, 37, 38, 37, 39, 37, 36, 38, 37, 40.
Size 37 comes up four times, more than any other size – it is the mode. - When two values come up the most times, equally often, both are modes.
The mean is the sum of the data, divided by the number of data.
- – the sum of all the data.
- – the number of data.
In its last five games the class football team scored 2, 0, 3, 1 and 4 goals:
- The sum: .
- There are 5 data, so the mean: goals a game.
The mean is what each one would get if the sum were shared out equally.
Four friends collected money for a present:
- Together they collected shekels.
- Had each given the same amount: shekels – and that is the mean.
- In the chart: what the bars taller than 35 have above it fills exactly what the shorter bars lack.
The mean can come out a number that is not among the data, even a number that is not whole.
Uri’s points in four basketball games: 4, 7, 5, 6.
Uri never scored 5.5 points in a game, but that is what he would have scored had he scored the same in every game.
The mode and the mean describe the data in different ways, and sometimes one of them fits better.
- Data that are words: pets have no mean – you cannot add a dog and a cat. They have only a mode.
- A shoe shop: the mean of the shoe sizes above is 37.5, and there is no such shoe. The shop needs the mode: it orders the most pairs in size 37.
- One very large value: the weekly pocket money of five friends is 20, 20, 25, 30 and 155 shekels.
The mean: shekels. The mode: 20 shekels.
Four of the five friends get less than 50 shekels: the 155 “pulls” the mean up, and it does not describe most of the friends well.
The median is the value in the middle, when the data are put in order from the smallest to the largest.
- The pocket money, in order: 20, 20, 25, 30, 155. The median is 25: two values are smaller, and two are larger.
- The 155 does not change the median: had it been 35, the median would still be 25.
- When the number of data is even, two values are in the middle, and the median is their mean. For 3, 5, 8, 10 the median is .
The marks of 10 pupils in a short quiz, out of 10:
8, 7, 9, 8, 10, 6, 8, 9, 5, 8
What is the mode?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
Work out the mean.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
On five days Maya read 12, 20, 15, 8 and 18 pages of a book.
How many pages did Maya read a day, on average?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
At a birthday party there are six children aged 7 and a grandfather aged 70.
What is the mean age at the party?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
What is the mode of the ages?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
Which describes the party better – the mean or the mode? Explain.
Find the median.
13, 8, 15, 10, 9
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
4, 9, 6, 11, 2, 7
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
Dana took four tests, and her marks were 80, 90, 75 and 95.
What mark does she need in the fifth test, so that the mean of all five tests is 86?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power