determine whether the following statement makes sense or does not make sense, and explain the reasoning. the…

determine whether the following statement makes sense or does not make sense, and explain the reasoning. the mean can be misleading if you dont know the spread of data items. choose the correct answer below. a. the statement does not make sense because the mean is the true center of the data. b. the statement makes sense because there may exist some outliers (maybe much greater or much less than the rest of the data) in the data items. c. the statement makes sense because mean is not always the true average of the data. d. the statement does not make sense because the mean measures the spread of the data items.

determine whether the following statement makes sense or does not make sense, and explain the reasoning. the mean can be misleading if you dont know the spread of data items. choose the correct answer below. a. the statement does not make sense because the mean is the true center of the data. b. the statement makes sense because there may exist some outliers (maybe much greater or much less than the rest of the data) in the data items. c. the statement makes sense because mean is not always the true average of the data. d. the statement does not make sense because the mean measures the spread of the data items.

Answer

Brief Explanations:

The mean is calculated as the sum of all data items divided by the number of data items. Outliers (extremely large or small values) can significantly affect the mean. For example, if we have data set ( {1,2,3,4,100} ), the mean is (\frac{1 + 2+3+4 + 100}{5}=\frac{110}{5} = 22). The value 100 (an outlier) pulls the mean upwards. Without knowing the spread (which would reveal the outlier), the mean of 22 might give a wrong impression of the "typical" value in the data set (most values are around 1 - 4).

  • Option A: The mean is not always the "true center" when there are outliers. So this option is incorrect.
  • Option B: Outliers can mislead the mean. If we know the spread (e.g., using range, inter - quartile range), we can better understand the data. This option is correct.
  • Option C: The mean is always the arithmetic average ((\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n})), but it can be misleading due to outliers. The reasoning in this option is not as precise as Option B.
  • Option D: The mean does not measure the spread. Measures of spread include range, variance, standard deviation. So this option is incorrect.

Answer:

B. The statement makes sense because there may exist some outliers (maybe much greater or much less than the rest of the data) in the data items.