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Does the mean or median better describe the shape of this data set? Enter 1 for mean or 2 for median.

3, 34, 36, 34, 6, 29, 30, 27, 39

(1 point)

1 answer

To determine whether the mean or median better describes the shape of the data set, we should first calculate both values.

  1. Mean:

    • Sum of the data: \(3 + 34 + 36 + 34 + 6 + 29 + 30 + 27 + 39 = 208\)
    • Number of values: \(9\)
    • Mean: \(\frac{208}{9} \approx 23.11\)

  2. Median:

    • First, we sort the data: \(3, 6, 27, 29, 30, 34, 34, 36, 39\)
    • The median is the middle value. For 9 values, the median is the 5th value, which is \(30\).

Now, let's compare:

  • The mean is about \(23.11\) and the median is \(30\).
  • The mean is lower than the median, indicating that the data might be skewed due to the low value of \(3\).

Generally, when there are outliers or the data is skewed, the median provides a better measure of central tendency because it is less affected by extreme values.

In this case, since the mean is affected by the outlier (the value \(3\)), the median is the better representation of the data set.

Therefore, the answer is:

2 (median).