Question 2

(a)    The table below lists the prices of apartments with 2 bedrooms and 2 bathrooms sold between January and July of 2018 in Australian state capital city centres (Sydney NSW 2000, Melbourne VIC 3000, Brisbane QLD 4000, Adelaide SA 5000, Perth WA 6000, and Hobart TAS 7000). The data are available in the website www.realestate.com.au/sold and the prices are given in thousand Australian dollars. Consider the information as sample data since some selling prices were undisclosed.

(b)    Compute the standard deviation, mean absolute deviation and range for each city.

(c)    Draw a box and whisker plot for the sold prices of each city and put them side by side on one graph with the same scale so that the sold prices for different cities can be compared. (This graph must be done in EXCEL or similar software and cannot be hand-drawn.)

Write a paragraph on 2 bed, 2 bath apartment prices of each city, number of apartments sold, and recent trends in apartment prices in the Australian capital cities after doing some research.

Apartments (2 bed, 2 bath) sold between Jan and Jul 2018 in Australian state capitals.
Capital city	Prices Sold (in thousand AUD)
Sydney NSW 2000	3680, 1825, 1110, 1190, 1850, 1165, 940, 1399, 1075, 1445, 1900, 2000, 2550, 2350, 1810, 1265, 2300, 1550, 2380
Melbourne VIC 3000	643, 1320, 600, 615, 895, 700, 610, 801,830, 600, 550, 645, 690, 733, 610, 608, 525, 700, 534, 625, 770, 1325, 1142, 650, 585, 680, 770, 675, 650, 580, 570, 1667, 790, 690, 870, 515, 821, 825, 560, 470, 621
Brisbane QLD 4000	750, 452, 502, 542, 620, 490, 455, 600, 625, 527, 820, 650, 550, 498, 355, 997, 498, 450, 420, 1010, 345, 445, 760, 485, 412, 435, 505, 730, 900, 650, 510, 827, 380, 358, 375, 600, 595, 615
Adelaide SA 5000	620, 595, 360, 530, 610, 1415, 485, 691, 458, 578, 820, 600, 725, 615
Perth WA 6000	650, 535, 440, 365, 445, 440, 480, 440, 460, 490, 430, 480, 470, 545, 628, 815, 520, 490
Hobart TAS 7000	615, 893, 637, 730, 810

From the information provided in the table above,

(a) Compute the mean, median, first quartile, and third quartile of sold prices for each city using the exact position, (n+1)f, where n is the number of observations and f the relevant fraction for the quartile