Where the values pile up
The mean and the median show the centre, where the values pile up.
A whole Grade 5 class
The heights of 28 students of a Grade 5 class are between 128 cm and 158 cm.
Where do you think most of the heights pile up?
What this lesson covers
The idea
The mean and the median are measures of central tendency: they represent the 'centre' of the data, around which the values tend to pile up.
A whole Grade 5 class
The heights of 28 students of a Grade 5 class are between 128 cm and 158 cm.
Where do you think most of the heights pile up?
- Near 130 cm
- Near 145 cm
- Near 155 cm
Catch the pile
Each dot is one student. Slide the yellow band, 10 cm wide, along the line. Find the place where it catches the most dots.
The centre of the data
The dots pile up around 145 cm. When you found that place, the mean and the median of the class were marked right inside it.
Both numbers tell us where the heights tend to pile up: the “centre” of the data.
The mean and the median are measures of central tendency: they represent the “centre” of the data, around which the values tend to pile up.
- Heights | Mean | Median
- Whole class | 144.5 | 145
- Boys | 142.94 | 144
- Girls | 146.9 | 148
Notes
The mean and the median are measures of central tendency: they represent the “centre” of the data, around which the values tend to pile up.
Check yourself
What do “measures of central tendency” tell us?
Which two of these are measures of central tendency?
Most of the heights in a class pile up between 140 cm and 150 cm. Which number is most likely to be the mean or the median?
Of the 28 students, 17 have heights from 140 cm to 150 cm. How many students are outside this range?
Answer: 11
28 − 17 = 11 students. Most students (17) are in the pile.
- The biggest and the smallest values. Those are the two ends of the data, not its centre.
- How many values there are. The number of values does not say where they pile up.
- The centre of the data, where the values tend to pile up — correct. Yes! They are numbers that stand for the middle of the data.
- Mean and median — correct. Yes! Both stand for the centre of the data.
- Minimum and maximum. These are the ends of the data, not its centre.
- Range and total. The range tells the spread and the total adds up all the values. Neither marks the centre.
- 128 cm. That is near the shortest student, far from where the heights pile up.
- 158 cm. That is near the tallest student, far from where the heights pile up.
- 145 cm — correct. Yes! It lies in the middle of the pile.