Step by step
The question
Question: describe the data 10, 11, 11, 11, 12, 15: its center, its spread and its shape.
10, 11, 11, 11, 12, 15
1 Draw a dot plot
A number line from 10 to 15.
One dot for each number.
10 first.
And so on.
2 Find the center
There are 6 numbers.
The middle is between number 3 and number 4.
= 6 numbers: middle = numbers 3 and 4
They are 11 and 11.
Halfway between is 11.
= center: median = 11
3 Find the spread
The spread: biggest minus smallest.
15 minus 10 is 5.
= spread: range = 15 − 10 = 5
4 Describe the shape
The tallest stack, the peak, is at 11.
One peak, at 11.
No dots at 13 and 14: a gap.
Most dots are on the left.
A few spread out to the right: a tail to the right.
= shape: peak at 11, gap at 13 and 14, tail to the right
5 Check
Let's check: we count the dots.
6 dots for 6 numbers.
Every number is crossed out.
So the dot plot is right, and so is the answer!
6 dots, 6 numbers
Let's look back.
First: draw a dot plot.
Then: find the center.
Then: find the spread.
Then: describe the shape.
Last: check.
Answer
= shape: peak at 11, gap at 13 and 14, tail to the right