Download Standardised Numbers

Standardised Numbers
Hayleigh 11B
Standardised Scores
Value - Mean
The Standardised Score =
Standard Deviation
They are usually based on normal curves which have 68% of the
data is in between -1 and +1 standard deviation of the mean. 95%
of all values lie between -2 and +2 standard deviations of the
mean and 99.7% lie within +/- 3 standard deviations of the mean.
Example
The mean and standard deviation of the marks in a Mathematics exam and in a Statistics exam are
shown. The marks in both exams are normally distributed.
Mean
Standard Deviation
Mathematics
63
6
Statistics
73
8
John scored 54 marks in the Maths exam and 57 in the Stats exam.
John claimed he was better at Maths. By standardising his marks decide if the data supports his claim.
Value - Mean
The Standardised Score =
Standard Deviation
Maths:
54 – 63
Stats:
57 – 73
6
= -1.5
8
= -2
This shows that John’s claim is valid
because -1.5 is closer to the mean for maths,
than -2 is for the mean of stats, so this shows
his scores are both lower than the mean and
the maths standardised score is closer to the
mean therefore indicating a better
performance in maths.
Standard Population
The standard population usually consists of 1000 people and is a
representative sample of the whole population. It is a stratified sample.
This means the size of each age group is represented equally.
Age group
Population
Age group
Standard Population
0-19
1056
0-19
1056/20414 x 1000 = 52
20-39
6294
20-39
6294/20414 x 1000 = 308
40-59
8458
40-59
8458/20414 x 1000 = 414
60+
4606
60+
4606/20414 x 1000 = 226
Total = 20414
You should then add the numbers up to check they add up
to 1000 which is the size of the sample of the population
that is usually required for a standard population.
Example
The populations of Liversedge and Outwood are made up as follows:
Age Group
Under 16
17 – 30
31 – 60
61 +
Outwood
6998
10645
11646
6432
Liversedge
7546
9536
12843
4927
Find the standard population for the towns
Add up the total populations. Outwood = 35721
Liversedge = 34852
For each age group and each town, divide the population by the total population and x by 1000.
Age Group
Under 16
17 – 30
31 – 60
61 +
Outwood
6998/35721 x 1000
= 196
10645/35721 x 1000
= 298
11646/35721 x 1000
= 326
6432/35721 x 1000
= 180
Liversedge
7546/34852 x 1000
= 216
9536/34852 x 1000
= 274
12843/34852 x 1000
= 369
4927/34852 x 1000
= 141
Compare the populations of the two towns.
You can comment on various things here such as the number of under 16s is higher in
Liversedge than in Outwood or that in Liversedge there are less people 61 years or older.
Standardised Birth/Death Rate
The standardised death rate is calculated using the standard
population of the whole country and the crude rate.
This is for each age
group and you add
them up
This is what you are finding
out. It is a more accurate
measure than the crude rate.
The Standardised Rate =
 (crude rate x standard population)
 standard population
This is the sum of the
whole standard
population for each age.