Question

Amanda collects 10 leaves, and measures their lengths, in centimeters. Here are her results:

5, 6, 5, 2, 4, 5, 8, 7, 5, 4

Combine the concepts of the mean and standard deviation of the leaves Amanda collected. What do you infer or deduce from the value of the mean and the standard deviation? What do those values, in other words, tell you about the lengths of the leaves in the collection?

Should Amanda use the dataset from her collection to speculate on the mean leaf length of the trees in a forest near her home? Why or why not?

Answer 1

From the given data set

Mean

= Sum of all observations / Total number of observations

= 5 + 6 + 5 + 2 + 4 + 5 + 8 + 7 + 5 + 4 / 10

= 5.1

Standard deviation

First arrange the dataset in ascending order as

2 , 4 , 4 , 5 , 5 , 5 , 5 , 6 , 7 , 8

= 1.6633

Inference :

It does Mean the representative single value of leaves 5.1 and

Spread or Variation among all leaves is 1.6633

Here Amanda can expect the length of leaves in future also. Because the expected mean value is nothing an Mean value.