248 261 268 273 275 279 282 283 284 284 287 288 289 292 293 296 296 299 310 504 Identify any outliers. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The outlier(s) is/are 504 pounds (Type a whole number Use a comma to separate answers as needed ) B. There are no outliers The median is 2855 pounds (Type an integer or decimal rounded to one decimal place as needed.) The untrimmed mean is square pounds (Type an integer or decimal rounded to one decimal place as needed.) The 10% trimmed mean is square pounds (Type an integer or decimal rounded to one decimal place as needed.)

Question

248 261 268 273 275 279 282 283 284 284 287 288 289 292 293 296 296 299 310 504 Identify any outliers. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The outlier(s) is/are 504 pounds (Type a whole number Use a comma to separate answers as needed ) B. There are no outliers The median is 2855 pounds (Type an integer or decimal rounded to one decimal place as needed.) The untrimmed mean is square pounds (Type an integer or decimal rounded to one decimal place as needed.) The 10% trimmed mean is square pounds (Type an integer or decimal rounded to one decimal place as needed.)

Answer 1

To identify any outliers in the given data set, we can use the Interquartile Range (IQR) method. First, let's arrange the data in ascending order:

Next, we need to find the median, which is the middle value of the data set. Since there are 20 values, the median will be the average of the 10th and 11th values:Median = (284 + 287) / 2 = 290.5Now, let's find the first quartile (Q1) and third quartile (Q3). Q1 is the median of the lower half of the data, and Q3 is the median of the upper half of the data.Q1 = Median of the lower half = 268Q3 = Median of the upper half = 288Now, we can calculate the Interquartile Range (IQR):IQR = Q3 - Q1 = 288 - 268 = 20To find the lower and upper bounds for potential outliers, we use the following formulas:Lower bound = Q1 - 1.5 * IQRUpper bound = Q3 + 1.5 * IQRLower bound = 268 - 1.5 * 20 = 238Upper bound = 288 + 1.5 * 20 = 318Any data points below the lower bound or above the upper bound are considered outliers.In this case, the only outlier is 504, which is above the upper bound of 318.So, the correct choice is A. The outlier(s) is/are 504 pounds.Now, let's calculate the untrimmed mean and the 10% trimmed mean.Untrimmed mean = (Sum of all data points) / (Total number of data points)Untrimmed mean = (248 + 261 + 268 + 273 + 275 + 279 + 282 + 283 + 284 + 284 + 287 + 288 + 289 + 292 + 293 + 296 + 296 + 299 + 310 + 504) / 20Untrimmed mean = 5555 / 20 = 277.7510% Trimmed Mean = (Sum of all data points excluding the 10% lowest and highest values) / (Total number of data points - 20%)10% Trimmed Mean = (Sum of all data points excluding 248 and 504) / 1810% Trimmed Mean = (261 + 268 + 273 + 275 + 279 + 282 + 283 + 284 + 284 + 287 + 288 + 289 + 292 + 293 + 296 + 296 + 299 + 310) / 1810% Trimmed Mean = 5055 / 18 = 280.83Therefore, the untrimmed mean is 277.75 pounds, and the 10% trimmed mean is 280.83 pounds.

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