Bats emit high-frequency sounds and listen for echoes to find prey. Until an insect is

detected, these pulses are emitted at a relatively slow rate; when an insect is detected the

pulse-to-pulse interval decreases dramatically. This makes it possible to find the range of

the bat's echolocation system by recording how far the bat is from the prey at the time that

the rate increases (something much easier said than done, of course!). The following

detection distances were collected for 11 "catches" (all distances in cm):

62 52 68 23 34 45 27 42 83 56 40

(a) Sketch a picture of the histogram you got.

(b) Go back to Window and change the bin size Xscl, trying both larger and smaller

values. Sketch two of the graphs that you get, one larger and one smaller. What do

you find? Which picture of the three you've done is most informative?

(c) A useful outgrowth of a histogram is something called a relative frequency histogram.

Here the vertical axis, instead of being counts of data points, is the relative frequency

of those data points in the set. (Remember that the relative frequency would be the

number of data points in that bin divided by the total number!) Make a relative

frequency histogram for this data using the bins from the histogram in (a). Hint: The

first bin has 2 of the 11 data points, so the first bar should have height 2 / 11 =.1818.

(d) Make a stem-and-leaf plot for this data.