This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — here are the answers to those questions: 8. The five numbers needed to construct a box and whisker plot are the minimum value, first quartile (Q_1), median (Q_2), third quartile (Q_3), and maximum value. 9. The interquartile range (IQR) in a box plot represents the middle 50% of the data. It is the range between the first quartile (Q_1) and the third quartile (Q_3), indicating the spread of the central portion of the dataset. 10. To find the cumulative frequency for the class 20-40: Step 1: Identify the frequencies for the classes up to and including 20-40. The frequency for 0-20 is 5. The frequency for 20-40 is 8. Step 2: Sum these frequencies. Cumulative frequency = 5 + 8 = 13 The cumulative frequency for the class 20-40 is 13. 11. The relationship between variance and standard deviation is that the standard deviation is the square root of the variance. Conversely, the variance is the square of the standard deviation. Both measure the spread or dispersion of a dataset. 12. MAD stands for Mean Absolute Deviation. 13. For the dataset: 5, 10, 15, 20, 25, calculate the mean absolute deviation (MAD). Step 1: Calculate the mean (x) of the dataset. x = (5 + 10 + 15 + 20 + 25)/(5) = (75)/(5) = 15 Step 2: Calculate the absolute deviation for each data point from the mean. |5 - 15| = |-10| = 10 |10 - 15| = |-5| = 5 |15 - 15| = |0| = 0 |20 - 15| = |5| = 5 |25 - 15| = |10| = 10 Step 3: Calculate the sum of the absolute deviations. |x_i - x| = 10 + 5 + 0 + 5 + 10 = 30 Step 4: Calculate the Mean Absolute Deviation (MAD). MAD = |x_i - x|n = (30)/(5) = 6 The mean absolute deviation (MAD) for the dataset is 6. Got more? Send 'em!