1. Identify each variable as quantitative or qualitative. 1.a) Amount of time it takes to assemble a simple puzzle is quantitative because it is measured numerically. 1.b) Number of students in a first grade class is quantitative because it is a countable number. 1.c) Rating of a newly elected politician (excellent, good, fair, poor) is qualitative because it describes categories or qualities. 1.d) State in which a person lives is qualitative because it is a category or label. 2. Construct a stem and leaf plot for the heart rate data: Data: 87, 109, 79, 80, 96, 95, 90, 92, 96, 98, 101, 91, 78, 112, 94, 98, 94, 107, 81, 96 Step 1: Organize data by tens digit (stem) and units digit (leaf): 7 | 8 9 8 | 0 1 7 9 | 0 1 2 4 4 5 6 6 6 7 8 8 10 | 1 7 9 11 | 2 This stem and leaf plot shows the distribution of heart rates. 3. For the set of numbers 6.5, 8.5, 4.7, 9.4, 11.3, 8.5, 9.7, 9.4: 3.a) Range = max - min = 11.3 - 4.7 = $6.6$ 3.b) Mean = sum of values / number of values $$\text{Mean} = \frac{6.5 + 8.5 + 4.7 + 9.4 + 11.3 + 8.5 + 9.7 + 9.4}{8} = \frac{67.9}{8} = 8.49$$ 3.c) Median: Sort data: 4.7, 6.5, 8.5, 8.5, 9.4, 9.4, 9.7, 11.3 Median = average of 4th and 5th values = $\frac{8.5 + 9.4}{2} = 8.95$ 3.d) Mean absolute deviation (MAD): Calculate absolute deviations from mean 8.49: $|6.5 - 8.49|=1.99$, $|8.5 - 8.49|=0.01$, $|4.7 - 8.49|=3.79$, $|9.4 - 8.49|=0.91$, $|11.3 - 8.49|=2.81$, $|8.5 - 8.49|=0.01$, $|9.7 - 8.49|=1.21$, $|9.4 - 8.49|=0.91$ Sum of absolute deviations = 1.99 + 0.01 + 3.79 + 0.91 + 2.81 + 0.01 + 1.21 + 0.91 = 11.64 MAD = $\frac{11.64}{8} = 1.46$ 3.e) Standard deviation (SD): Calculate squared deviations: $(6.5 - 8.49)^2 = 3.96$, $(8.5 - 8.49)^2 = 0.0001$, $(4.7 - 8.49)^2 = 14.36$, $(9.4 - 8.49)^2 = 0.83$, $(11.3 - 8.49)^2 = 7.91$, $(8.5 - 8.49)^2 = 0.0001$, $(9.7 - 8.49)^2 = 1.46$, $(9.4 - 8.49)^2 = 0.83$ Sum of squared deviations = 3.96 + 0.0001 + 14.36 + 0.83 + 7.91 + 0.0001 + 1.46 + 0.83 = 29.35 Variance = $\frac{29.35}{8} = 3.67$ SD = $\sqrt{3.67} = 1.92$ Final answers: - Range: $6.6$ - Mean: $8.49$ - Median: $8.95$ - Mean absolute deviation: $1.46$ - Standard deviation: $1.92$