Question

My Notes Ask Your Te Although bats are not known for their eyesight, they are able to locate prey (mainly insects) by emitting high-pitched sounds and listening for echoes. A paper gave the following distances (in centimeters) at which a bat first detected a nearby insect. 23 40 52 68 42 45 27 63 56 83 34 (a) Compute the sample mean distance at which the bat first detects an insect. (Round your answer to three decimal places.) cm (b) Compute the sample variance and standard deviation for this data set. (Round your answers to two decimal places.) Variance Standard deviation

Answer 1

a)

Sample size = n = 11

Sum of all samples = 533

Sample mean is

$\bar{x}=\frac{\sum x}{n}=\frac{533}{11}=48.455$

b)

$Variance =Var(X)=\frac{\sum (x-\bar{x})^{2}}{n-1}$

x	x-xbar	(x-xbar)^2
23	-25.455	647.9339
40	-8.455	71.47934
52	3.545	12.57025
68	19.545	382.0248
42	-6.455	41.66116
45	-3.455	11.93388
27	-21.455	460.2975
63	14.545	211.5702
56	7.545	56.93388
83	34.545	1193.388
34	-14.455	208.9339
	Total	3298.727

$Var(X)=\frac{\sum (x-\bar{x})^{2}}{n-1}=\frac{3298.727}{11-1} =329.873$

Variance = 329.873

Standard deviation is square root of variance.

$SD=\sqrt{Var(X)}=\sqrt{329.873}=18.162$

Standard deviation = 18.162