Question

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

769 691 699 730 711 765 702 718 719 712 768 688 757
695 768 735 709 758 708 693 736 700 687 772 715
a. Find the mean, median and mode of this information. (Round your answers to 2 decimal places.)
b. What are the range and standard deviation? (Round your answers to 2 decimal places.)
c. Use the Empirical Rule to establish an interval which includes about 95 percent of the observations. (Round your answers to 2 decimal places.)

Answer 1

A.

mean = 724.2

Median = 715

Mode = 768

B.

Range = 85

Standard deviation = 29.30

C.

Interval = [665.6, 782.8]

Explanation:

Number of samples n = 25

Summation X= 769 + 691 + 699 +730+711+ 765+ 702 718 +719 +712+ 768 +688 +757+695 768 +735 +709 +758 +708+ 693 +736 700+ 687 +772 +715 = 18105

A.

1. Mean = 18105/25

= 724.2

2. Median is the middle value when arranged from the least value to the highest = 715

3. Mode is the number with the highest frequency = 768 (occured two times)

B.

1. Range = highest value - lowest value

Highest value = 772

Lowest value = 687

772-687 = 85

2. Standard deviation = √(X-barX)²/n-1

= √20604/25-1

=√858.5

= 29.30

Please check attachment for the full calculation of the standard deviation

C.

Interval

[Mean - 2(sd), mean + 2(sd)]

= [724.2-2x29.3, 724.2+2x29.3]

=[665.6, 782.8]