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The 5 number summary and IQR have been calculated for you. Min: \( 0 \quad \) Q1:4 Median:9 Max:95 Leave your answers as decimals if needed. Don't round. The low end value is The high end value is Does this data set have outliers? Type Yes or No Ther

Ask by Sanders George. in the United States
Mar 09,2025

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Answer

There are no outliers in the data set.

Solution

To determine if the data set has outliers, we need to compare the low end value and the high end value with the 5 number summary (Min, Q1, Median, Q3, Max) provided. Given: Min: 0 Q1: 4 Median: 9 Max: 95 The low end value is 0 and the high end value is 95. To determine if there are outliers, we need to check if any data points are more than 1.5 times the interquartile range (IQR) away from the first quartile (Q1) or the third quartile (Q3). The IQR is calculated as Q3 - Q1. Q3 = 95 (Max) Q1 = 4 IQR = Q3 - Q1 = 95 - 4 = 91 Now, we check if any data points are more than 1.5 times the IQR away from Q1 or Q3. Lower bound = Q1 - 1.5 * IQR = 4 - 1.5 * 91 = 4 - 136.5 = -132.5 Upper bound = Q3 + 1.5 * IQR = 95 + 1.5 * 91 = 95 + 136.5 = 231.5 Since the low end value (0) is less than the lower bound (-132.5) and the high end value (95) is less than the upper bound (231.5), there are no outliers in the data set. Therefore, the answer is: No

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Bonus Knowledge

To determine the low-end value, use the formula for identifying outliers: \( Q1 - 1.5 \times IQR \). Given Q1 is 4 and the IQR (Interquartile Range) can be assumed from the range between Q1 and the maximum. For the high end, use the formula \( Q3 + 1.5 \times IQR \) (assuming Q3 can be inferred from the median). You can then check if any data points fall outside these bounds. If they do, there are outliers present in the dataset. In this scenario, without specific values of Q3 or IQR, further numerical values can’t be established, but to answer your last question directly—based on the five-number summary, if the calculated bounds determine points outside the range specified, then type "Yes" for outliers, if not, type "No".

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