Standard deviation — Algebra I · Grade 9 or accelerated Grade 8, what it means and where it is taught
A measure of typical distance from the mean.
Taught in Algebra I · Grade 9 or accelerated Grade 8.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Mean — Two kinds of centre: the balance point, and the middle value.
What uses it later
This idea is needed for:
- Normal distribution — The symmetric bell-shaped distribution described by its mean and standard deviation.
- z-score — How many standard deviations a value sits from the mean: z = x - μσ.
Practise this idea
5 questions in the course bank use Standard deviation, in Statistics: Centre, Spread & Displays, The Normal Distribution.
Problem 1
Which pair of statistics is resistant to outliers?
- Median and IQR
- Mean and standard deviation
- Mean and range
- Median and range
Worked answer
Median and IQR
Median ignores the extremes
IQR uses only the middle half
Mean, range and standard deviation all move a lot
Problem 2
A data set has mean 50. Every value is increased by 8. Find the new mean and the new standard deviation, given the old one was 6.
Worked answer
mean 58, sd 6
Every value up 8, so the mean is 58
Distances between values are unchanged
So the standard deviation is still 6
Problem 3
Using the empirical rule, approximately: what percent of a normal population lies within one standard deviation of the mean?
Worked answer
68
About 68%
Problem 4
Using the empirical rule, approximately: what percent lies within two standard deviations?
Worked answer
95
About 95%
Problem 5
Using the empirical rule, approximately: what percent lies within three standard deviations?
Worked answer
99.7
About 99.7%