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compute the standard deviation and variance

1.) 10, 11, 12, 13, 14
2.) 8, 8, 4, 4
3.) 3, 5, 7, 9​


Sagot :

Answer:

  1. variance = 2 ; standard deviation = 1.41
  2. variance = 4 ; standard deviation = 2
  3. variance = 6 ; standard deviation = 2.24

Step-by-step explanation:

1.

mean = 10 + 11 + 12 + 13 + 14 / 5

= 60 / 5

mean = 12

variance (σ²) = (-2)² + (-1)² + 0² + 1² + 2² /5

= 4 + 1 + 0 + 1 + 4 / 5

= 10 / 5

σ² = 2

standard deviation = √2

σ = 1.41

2.

mean = 8 + 8 + 4 + 4 / 4

= 24 / 4

mean = 6

variance (σ²) = 2² + 2² + (-2)² + (-2)² / 4

= 4 + 4 + 4 + 4 / 4

= 16 / 4

σ² = 4

standard deviation = √4

σ = 2

3.

mean = 3 + 5 + 7 + 9 / 4

= 24 / 4

mean = 6

variance (σ²) = (-3)² + (-1)² + 1² + 3² / 4

= 9 + 1 + 1 + 9 / 4

= 20 / 4

σ² = 5

standard deviation = √5

σ = 2.24