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Application {13 marks} 32. A consumer magazine evaluated 40 models of bathroom scales. The table below lists the prices for these models (rounded to the nearest dollar). Use technology (graphing calculator, spreadsheet, Fathom, online stats calculator etc.) when appropriate in this question (a) and b) for sure). Please state what you have used. Scale Model Price ($) Scale Model Price ($) EconoHealth A10 50 Superskale 6400 65 Econo Health A 12 50 Superskale 7200 20 EconoHealth B10 50 Superskale 8000 14 Econo Health E10 28 Superskale 8280 25 EconoHealth Digital-10 65 SvelteChek 12300 24 EconoHealth E-20 40 SvelteChek 12400D 48 EconoHealth E-30 50 SvelteChek 12509 15 HealthSkale 190 22 SvelteChek 12510 10 HealthSkale 210 32 SvelteChek Fashion 17 HealthSkale 211 30 SvelteChek Pro 50 HealthSkale 290 Deluxe 79 SvelteChek Xtra 25 HealthSkale 310 50 Weighbeter 550 22 HealthSkale 1000 23 Weighbeter 801D 60 HealthSkale 1002 20 Weighbeter 830 30 HydroXact 12573 35 Weighbeter 835 30 HydroXact 12756 24 Weighbeter 950 10 HydroXact 12856 25 Weighbeter 2000 12 Prowt P10A 120 Weighbeter 2100 20 Prowt Value 35 Weighbeter Basic 12 Prowt Value 2 35 Weighbeter PLUS 50 a) i)Find the median, first quartile, and third quartile for the prices of these bathroom scales. {A - 3 marks} ii) Draw a box and whisker plot by hand for the data. ( or import /screen capture one from a program) {A - 2 marks} b ) Calculate the mean, standard deviation, and variance for the prices of these bathroom scales.c) i) Determine the z-score for the price of each scale below: {A -3 marks) SvelteChek Pro? Weighbeter Basic? ii) Explain the difference between a positive and negative z-score using a single sentence. d) Find the range and the interquartile range for the prices of these bathroom scales. {A - 2 marks}