Estimate (a) Mean (b) Quartiles (c) What is the probability a random burrow dept
ID: 3352454 • Letter: E
Question
Estimate (a) Mean (b) Quartiles (c) What is the probability a random burrow depth is between 10 to 15 cm? (You are using part of bars and not the whole bar on the ends) 2.143 The Coruro's Burow. The subterrancan coruro (Spalacopus cyanus) is a social rodent that lives in large colonies in underground burrows that can reach lengths of up to 600 meters. Zoologists S. Begalil and M. Gallardo studied the characteristics of the burrow systems of the subterranean coruro in central Chile and published their findings in the Journal of Zoology, London (Vol. 251, pp. 53-60). A sample (A denisity scale is given instead of a frequency histogram 0.16 Denstiy 0.12 0.08 0.04 6.75 9.75 12.75 5.75 18.75 Depth (cm)Explanation / Answer
The histogram is converted into the following frequency distribution with relative frequency.
Class
Number
(i)
Class Interval
Mid-point
(xi)
Density
(As given)
Relative
Frequency
(ri)
Cumulative
Relative
Frequency
1
(6.75 – 8.25]
7.5
0.015
0.0225
0.0225
2
(8.25 – 9.75]
9.0
0.015
0.0225
0.045
3
(9.75 – 11.25]
10.5
0.015
0.0225
0.0675
4
(11.25 – 12.75]
12.0
0.09
0.135
0.2025
5
(12.75 – 14.25]
13.5
0.11
0.165
0.3675
6
(14.25 – 15.75]
15.0
0.15
0.225
0.5925
7
(15.75 – 17.25]
16.5
0.15
0.225
0.8175
8
(17.25 – 18.75]
18.0
0.08
0.12
0.9375
9
(18.75 – 20.25]
19.5
0.04
0.06
0.9975
Total
-
-
-
0.9975
Part (a)
Mean = [1,9](xi x ri)
= 14.8725 ANSWER
Part (b)
First Quartile, Q1 = 12.75 + {(0.25 – 0.2725) x (0.165/1.5)} = 12.756 ANSWER 1
Second Quartile = Median = 14.25 + {(0.5 – 0.3675) x (0.225/1.5)} = 14.270 ANSWER 2
Third Quartile = Q3 = 15.75 + {(0.75 – 0.5925) x (0.225/1.5)} = 15.774 ANSWER 3
Part (c)
Probability the depth is between 10 to 15 = Relative frequency for (10 - 15)
= Relative frequency for (10 – 11.25) +
Relative frequency for (11.25 – 14.25) +
Relative frequency for (14.25 - 15)
= {0.015 x (1.25/1.5)} + 0.2 + {0.15 x (0.75/1.5)}
= 0.0125 + 0.2 + 0.075
= 0.2875 ANSWER
Class
Number
(i)
Class Interval
Mid-point
(xi)
Density
(As given)
Relative
Frequency
(ri)
Cumulative
Relative
Frequency
1
(6.75 – 8.25]
7.5
0.015
0.0225
0.0225
2
(8.25 – 9.75]
9.0
0.015
0.0225
0.045
3
(9.75 – 11.25]
10.5
0.015
0.0225
0.0675
4
(11.25 – 12.75]
12.0
0.09
0.135
0.2025
5
(12.75 – 14.25]
13.5
0.11
0.165
0.3675
6
(14.25 – 15.75]
15.0
0.15
0.225
0.5925
7
(15.75 – 17.25]
16.5
0.15
0.225
0.8175
8
(17.25 – 18.75]
18.0
0.08
0.12
0.9375
9
(18.75 – 20.25]
19.5
0.04
0.06
0.9975
Total
-
-
-
0.9975
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