Environmental Science: Numerical Questions – Statistics Sd and Sem

Dr. Manishika Jain- Join online Paper 1 intensive course. Includes tests and expected questions.

Type I – Standard Deviation

1. In a city, the daily per capita inhalation (m3) values of contaminated air over a period of 5 days are 6.3,6.3,6.2,6.4 and 5.8, respectively. The sample mean with standard deviation of the data is

  1. 6.2 ± 0.02
  2. 6.2 ± 0.23
  3. 6.0 ± 0.15
  4. 6.2 ± 0.18

Answer: (B) 6.2 ± 0.23

Explanation: Mean =

=

=

= = 6.2

Standard Deviation =

Standard Deviation
6.36.3 - 6.2 = 0.10.01
6.36.3 - 6.2 = 0.10.01
6.26.2 - 6.2 = 00
6.46.4 - 6.2 = 0.20.04
5.85.8 - 6.2 =-0.40.16
Σ 0.22

Type II – Standard Error of Mean

2. In random samples of 64 boats out of a total 2400 boats, the mean number of defective boats is 3.2 with a sample standard deviation 0.8. The standard error of the mean is

  1. ~0.107
  2. ~0.40
  3. ~0.97
  4. ~0.097

Answer: (D) ~0.97

Explanation: Standard Error of Mean (SEM) =

=

= 0.8/8

= 0.1

Type III – Sample Size

3. If the standard deviation of a population is 20 and the standard error of mean is 4, then the sample size is:

  1. 25
  2. 80
  3. 5
  4. 100

Answer: (A) 25

Explanation: Standard Error of Mean (SEM) =

4 =

= 20/4 = 5

S0, n = (5) 2 = 25

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