# 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 (m^{3}) 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

6.2 ± 0.02

6.2 ± 0.23

6.0 ± 0.15

6.2 ± 0.18

Answer: (B) 6.2 ± 0.23

Explanation: Mean =

=

=

= = 6.2

Standard Deviation =

| 6.3-6.2 = 0.1 | 0.01 |

| 6.3-6.2 = 0.1 | 0.01 |

| 6.2-6.2 = 0 | 0 |

| 6.4-6.2 = 0.2 | 0.04 |

| 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

~ 0.107

~ 0.40

~ 0.97

~ 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:

25

80

5

100

Answer: (A) 25

Explanation: Standard Error of Mean (SEM) =

4 =

= 20/4 = 5

S0, n= (5)^{2} = 25

-Mayank