Question

Ch 4: 18 Amorphophallus johnsonii is a plant growing in West Africa, and it is better known as a “corpse-flower”. Its common name comes from the fact that when it flowers, it gives off a “powerful aroma of rotting flesh and faeces” (Beath, 1996). The flowers smell this way because their principal pollinators are carrion beetles who are attracted to such a smell. Beath (1996) observed that the number of carrion beetles (Phaeochrous amplus) that arrive per night to flowers of this species. The data are as follows:

51, 45, 61, 76, 11, 117, 7, 132, 52, 149

d) If you had been given 25 data points instead of 10, would you expect the mean to be greater, less than or about the same as the mean of this sample?

Greater than

e) If you had been given 25 data points instead of 10, would you expect the standard deviation to be greater, less than or about the same as this sample?

Less than  

For the above two answers my answers were wrong. It was supposed to be "about the same". Can someone please explain to be me the reasoning behind this? I don't understand how mean would not increase with more data points and how standard deviation would not decrease.  

Answer 1

The given data is from a sample. If the given data were collected randomly then we would not expect the mean or standard deviation to change when we increase the sample size. Because, we would expect the similar numbers from the data of extra values as well. Therefore, we can't expect the mean and standard deviation to vary.