Question

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.

63 23 27 68 52 34 42 42 56 45 83

Compute the sample mean distance at which the bat first detects an insect. (Round the answer to three decimal places.)

Compute the sample variance and standard deviation for this data set. (Round all answers to two decimal places.)

Compute the sample variance and standard deviation for new data set. (Round all answers to two decimal places.)

Answer 1

The mean value of the data set is 493 10 p 49.3 xplanation The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have: Sum of terms MeanNmber of erms In this example: Sumofterms-63+23 +27+68+52 + 34 Number of terms = 10 42 + 56 + 45 +88-493 Sum of terms Number of terms ean = Mean 10 27 34 42 45 52 56 63 68 49.3

ơ-18.9153 Explanation To find standard deviation we use the following formula We will compute this formula in 4 step:s Step 1: Find the mean. [ In this example: X49.3. (use this calculator for step by step explanation on how to find mean) Step 2: Create the following table data-mean 13.7 26.3 22.3 18.7 2.7 15.3 (data mean) data 63 23 27 68 52 34 42 56 45 83 187.69 691.69 497.29 349.69 7.29 234.09 53.29 44.89 18.49 1135.69 33.7 Step 3: Find the sun of numbers in the last column to get Σ(n-x)2 =3220.1 Step 4: Calculate ơ using the above formula 3220.1 10-1 18.9153

Variance = 3220.1/9=357.79