A sample consisting of five observations has an arithmetic mean of 12 and a median of 14. What is the smallest value that the range (largest observation minus smallest) can assume for such a sample?

5

Step-by-step explanation:

In the sample:

Median=14

Mean=12

Since the median is 14, to get the minimum range, we keep the values after the median as small as possible.

Therefore our numbers are:

*,*,14,14,14

The first number must be as large as possible.

Therefore:

Let x be the number

CrisCros multiply

2x+42=5*12

2x=60-42

2x=18

Divide both sides by 2

x=9.

Therefore, the five observations are:

9,9,14,14,14

Therefore, the smallest range

=14-9

=5

an advantage of the standard deviation is that it increases as the dispersion of the data increases. e. the interquartile range is preferred when the data are not skewed or no have outliers. an advantage of the standard deviation is that it uses all the observations in its computation.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)