Question

A sample of 25 undergraduates reported the following dollar amounts of entertainment expenses last year:

734 769 687 689 759 752 739 694 736 700 768 693 713
732 712 700 707 730 711 700 703 710 682 753 706
a. Find the mean, median and mode of this information. (Round your answers to 2 decimal places.)
Mean $
Median $
Mode (Click to select)$700$712$694
b. What are the range and standard deviation? (Round your answers to 2 decimal places.)
Range $
Standard deviation $
c. Use the Empirical Rule to establish an interval which includes about 95 percent of the observations. (Round your answers to 2 decimal places.)
The interval is from $ up to $ .
Expense
734
769
687
689
759
752
739
694
736
700
768
693
713
732
712
700
707
730
711
700
703
710
682
753
706

Answer 1

a) The mean μ = 719,16

The median is the middle number m = 711

The mode is the number that occurs more often

md = 700

b) The range r = 67

The standard deviation σ = 25.63

I ( 95 % ) = ( 667.90 ; 770.42)

Explanation:

We order the set of numbers in ascending order

682 687 689 693 694 700 700 700 703 706 707 710 711 712 713 730 732 734 736 739 752 753 759 768 769

The mean μ = Σ xi/n

μ = 719,16

The median is the middle number

m = 711

The mode is the number which occurs more often

md = 700

The range is r = 769 - 682 r = 67

c) Interval with 95 % of observations is ( μ + 2σ ; μ- 2σ )

I = ( 719.16 - 2*25.63 ; 719.16 + 2*25.63)

I ( 95 % ) = ( 667.90 ; 770.42)