객관식
Which of the following best describes the in a ?
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3. Describing Data Numerically
Mean
객관식
Which of the following best describes the effect of outliers on the of a data set?
A
Outliers have no effect on the and only affect the .
B
Outliers make the equal to the .
C
Outliers can significantly increase or decrease the , making it less representative of the central tendency of the data.
D
Outliers always decrease the , regardless of their value.
검증된 단계별 안내1
Step 1: Understand what an outlier is — an outlier is a data point that is significantly different from the other observations in the data set, either much larger or much smaller.
Step 2: Recall the definition of the mean — the mean is the sum of all data values divided by the number of values, expressed as \(\text{mean} = \frac{\sum x_i}{n}\).
Step 3: Consider how adding an outlier affects the sum — since the mean depends on the total sum, an extremely large or small outlier will increase or decrease the sum substantially.
Step 4: Recognize that because the mean is sensitive to every value, outliers can pull the mean toward themselves, making it less representative of the typical data point.
Step 5: Contrast this with the median, which is the middle value and less affected by extreme values, explaining why outliers impact the mean more than the median.
