Question

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 measures the spread of the data items. b. the statement makes sense because mean is not always the true average of the data. c. 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. d. the statement does not make sense because the mean is the true center of the data.

Explanation:

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 greatly affect the mean. For example, if we have data set \( \{1,2,3,4,100\} \), the mean is \(\frac{1 + 2+3+4 + 100}{5}=\frac{110}{5} = 22\). Here, the outlier 100 pulls the mean upwards. Without knowing the spread (which would reveal the outlier), the mean (22) might give a wrong impression of the "typical" value (most values are around 1 - 4). The mean does not measure the spread (measures like range, variance, or standard deviation do that), so option A is wrong. The mean is a type of average (sum of data/number of data), but it can be skewed by outliers. Option B is too vague. Option D is wrong because the mean is not always the "true center" (especially with outliers).

Answer:

C. 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.