1. Standard Deviation For a Sample of Data
We will use this version because it is easier to use for small samples.
Standard Deviation
For a Sample of Data
In real life situations it is normal to work with a sample
of data ( survey / questionnaire ).
We can use two formulae to calculate the sample deviation.
s = standard deviation
∑ = The sum of
x = sample mean
n = number in sample

2. 592 ÷ 8 = 74 Standard Deviation For a Sample of Data
Eight athletes have heart rates
70, 72, 73, 74, 75, 76, 76 and 76.
Step 2 : Calculate the mean :
592 ÷ 8 = 74
Step3: Calculate the sample deviation then their squares
Step 1 :
Sum all the values
Standard Deviation
For a Sample of Data
Totals
Heart Rate Deviation Deviation2
Step4: Use the formula to calculate the standard deviation 70 -4 16 72 -2 4
Calculate the sum of the squared deviations 73 -1 1 74 75 1 1 76 2 4 2 76 4 76 2 4
12-Jul-19

3. Calculate the mean :
720 ÷ 8 = 90
Example 1b : Eight office staff train as athletes.
Their Pulse rates are 80, 81, 83, 90, 94, 96, 96 and 100 BPM
Heart rate (x) 80 81 83 90 94 96
100
-10
100 -9 81 -7 49 4 16 36 6 6 36 10
100
∑x = 720

4. Who are fitter the athletes or staff. Staff data is more spread out.
Compare means
What does the deviation tell us.
Staff data is more spread out.
Athletes are fitter
Athletes
Staff
Mean = 74 bpm
Mean = 90 bpm
Std Dev = 2·20 bpm
Std Dev = 7·73 bpm