Answer:
Standard deviation = 0.59
Step-by-step explanation:
Given data → 5.6, 5.2, 4.6, 4.9, 5.7, 6.4
Mean of the given data = [tex]\frac{5.6+5.2+4.6+4.9+5.7+6.4}{6}[/tex]
= 5.4
Data (x) (x - mean) (x - mean)²
5.6 5.6 - 5.4 = 0.2 (0.2)² = 0.04
5.2 5.2 - 5.4 = -0.2 (-0.2)² = 0.04
4.6 4.6 - 5.4 = -0.8 (-0.8)² = 0.64
4.9 4.9 - 5.4 = -0.5 (-0.5)² = 0.25
5.7 5.7 - 5.4 = -0.3 (-0.3)² = 0.09
6.4 6.4 - 5.4 = 1 (1)² = 1
N = 6 [tex]\sum (x-mean)^2[/tex] = 2.06
Since, Standard deviation = [tex]\sqrt{\frac{\sum (x-mean)^2}{N}}[/tex]
= [tex]\sqrt{\frac{2.06}{6} }[/tex]
= 0.5859
≈ 0.59
