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

6.3

6.3-6.2 = 0.1

0.01

6.3

6.3-6.2 = 0.1

0.01

6.2

6.2-6.2 = 0

0

6.4

6.4-6.2 = 0.2

0.04

5.8

5.8-6.2 = -0.4

0.16

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