Answer :

The standard deviation of the number of days absent is found as 1.1616.

Define the term standard deviation?

  • The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean.
  • A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

For the stated question-

Number of Days Absent/Probability

  • 0 -  0.60
  • 1 - 0.20
  • 2 - 0.12
  • 3 - 0.04
  • 4 -  0.04
  • 5-  0.00

Thus, the mean is found as;

Mean = (0x0.60) + (1x0.20) + (2x0.12) + (3x0.04) + (4x0.04)

Mean = 0.72

Standard deviation σ = (0-0.72)² x 0.60 + (1-0.72)² × 0.20 + (2-0.72)² × 0.12 + (3-0.72)²  × 0.04 + (4-0.72)² × 0.04

Standard deviation  = 1.1616

Thus, the standard deviation of the number of days absent is found as 1.1616.

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The complete question is-

A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month.

Number of Days Absent/Probability

0 0.60

1 0.20

2 0.12

3 0.04

4 0.04

5 0.00

What is the standard deviation of the number of days absent?