# Environmental Science: Numerical Questions – Statistics Sd and Sem

Get unlimited access to the best preparation resource for UGC : Get detailed illustrated notes covering entire syllabus: point-by-point for high retention.

## 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

Explanation: Mean =

=

=

= = 6.2

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

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

Explanation: Standard Error of Mean (SEM) =

4 =

= 20/4 = 5

S0, n= (5)2 = 25

Developed by: