1. The problem involves understanding concepts of data management such as quartiles, deciles, percentiles, median, range, interquartile range (IQR), and mean absolute deviation (MAD). 2. Quartiles divide data into four equal parts. Q1 is the lower quartile (25th percentile), Q2 is the median (50th percentile), and Q3 is the upper quartile (75th percentile). 3. Deciles divide data into ten equal parts, and percentiles divide data into one hundred equal parts. 4. The median is equivalent to Q2, the fifth decile (D5), and the 50th percentile (P50). 5. The range is the difference between the greatest and least number in a data set. 6. The interquartile range (IQR) is the distance between Q1 and Q3, representing the middle 50% of the data. 7. Mean absolute deviation (MAD) measures the average distance between each data value and the mean, describing variability. 8. Example calculations: - Lower quartile (Q1) of 6,7,8,9,11,13,15: Arrange data, median of lower half is 7. - Upper quartile (Q3) of 136,150,119,150,125,140: Sort data 119,125,136,140,150,150; Q3 is median of upper half (140,150,150), which is 150. - Range of Ervin's scores 155,165,138,172,127,193,142: Max 193, Min 127, Range = 193 - 127 = 66. - Interquartile range of 17,18,18,19,20,21,21,23,25: Q1=18, Q3=21, IQR=21-18=3. - Mean absolute deviation of 2.50,3.75,1.25,2.25,3.00: Mean = 2.55, deviations = |2.50-2.55|+|3.75-2.55|+|1.25-2.55|+|2.25-2.55|+|3.00-2.55| = 0.05+1.20+1.30+0.30+0.45=3.3; MAD = 3.3/5=0.66. Final answers to key questions: - Techniques dividing data into equal groups: Quartiles, Deciles, Percentiles. - Median equivalent: all of these (Q2, D5, P50). - Score points dividing distribution into four parts: Quartiles. - Q1 is Lower Quartile. - Q1 corresponds to 25%. - Lower quartile of given scores: 7. - Quartile 3 is Upper Quartile. - Q3 corresponds to 75%. - Upper quartile of given data: 150. - Score points dividing into ten parts: Deciles. - D6 corresponds to 60%. - Score points dividing into hundred parts: Percentiles. - Scoring at 55th percentile means 55% scored same or worse. - Median is 50th percentile. - 75th percentile is third quartile. - Range is difference between greatest and least number. - Finding range: difference between max and min. - Range of Ervin's scores: 66. - Adding constant to data does not change range. - IQR is distance between Q1 and Q3. - IQR is range of middle 50%. - IQR stands for interquartile range. - IQR of given data: 3. - MAD describes average distance from mean. - MAD stands for Mean Absolute Deviation. - MAD of given data: 0.66. - MAD of amusement park ages: 4.8. - Highest MAD shows most variability; lowest shows most consistency.