Question

The index of biotic integrity (IBI) is a measure of the water quality in streams. II and land-use measures for a collection of streams in the Ozark Highland ecoregion of Arkansas were collected as part of a study The data table below gives the data for 11, the percent of the watershed that was forest, and the area of the watershed in square kilometers for streams in the original sample with watershed are less than or equal to 70km? Area Forest IBI Area Forest IBI Area Forest 181 Area Forest IBI 21 0 29 0 61 31 39 32 0 59 34 0 72 34 0 76 3 85 52 3 89 7 74 20 8 89 6 9 33 28 10 46 21 10 32 59 11 80 69 14 80 47 17 78 8 17 53 18 8 41 58 84 21 38 54 22 10 25 62 57 31 55 18 32 29 19 33 29 78 54 5 39 33 71 55 41 58 59 71 9 49 33 23 31 16 52 18 71 21 52 32 75 59 64 75 34 79 60 82 26 10 54 68 63 9 41 82 80 12 23 82 79 89 27 83 86 21 26 85 90 56 16 100 95 79 26 67 95 100 91 (a) Use numerical and graphical methods to describe the variable 101. Do the same for area. (Round your answers for to two decimal places and your answers for to three decimal places) ISI: TE 517.53 area area 18.00 K X X X S TV2/2000

Answer 1

The mean is given by :

Σ=1 X, n

and the standard deviation is given by : $s = \sqrt{\frac{\sum_{i=1}^{n}(X_{i} - \overline{X})}{n}}$

where n is the sample size

For IBI :

1. $\overline{X}_{IBI} = \frac{855}{12} = 71.25$      

2. $s_{IBI} = \sqrt{\frac{1876.25}{12}} = 12.50$

For area:

1.

arca 394 = 32.83 12

2.$s_{area} = \sqrt{\frac{4865.66}{12}} = 20.13$

Area 80 70 60 50 40 АЛ 30 20 10 0 0 4 UD N 8 10 12 14