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.
ScanSolve AI Answer
To solve question 10, we need to find the interquartile range (IQR) and the semi-interquartile range (SIQR) of the given height distribution. The height data is: 17, 16, 19, 18, 17, 18, 17, 19, 16, 19. There are n=10 data points. Step 1: Order the data from least to greatest. 16, 16, 17, 17, 17, 18, 18, 19, 19, 19 Step 2: Calculate the first quartile (Q_1). Q_1 is the median of the lower half of the data. Since n=10 is an even number, the lower half consists of the first n/2 = 5 values. Lower half: 16, 16, 17, 17, 17 The median of these 5 values is the middle value, which is 17. So, Q_1 = 17 inches. Step 3: Calculate the third quartile (Q_3). Q_3 is the median of the upper half of the data. The upper half consists of the last n/2 = 5 values. Upper half: 18, 18, 19, 19, 19 The median of these 5 values is the middle value, which is 19. So, Q_3 = 19 inches. Step 4: Calculate the Interquartile Range (IQR). The IQR is the difference between the third quartile and the first quartile. IQR = Q_3 - Q_1 IQR = 19 - 17 = 2 inches Step 5: Calculate the Semi-Interquartile Range (SIQR). The SIQR is half of the interquartile range. SIQR = IQR2 SIQR = (2)/(2) = 1 inch The interquartile range is 2 inches and the semi-interquartile range is 1 inch. The final answer is Interquartile Range: 2 inches, Semi-Interquartile Range: 1 inch. That's 2 down. 3 left today — send the next one.