Questions: Which of these are measures of central tendency that can be found for this list of heights recorded in the high-jump event at a track meet? Check all that apply. 4' 9'', 5' 3'', 5' 4'', 5' 7'', 5' 3'', 5' 99'', 6' 0'', 5' 4'', 6' 0'', 6' 1'', 5' 7'', 5' 5'', 4' 5'' A. Standard deviation B. Mode C. Mean D. Range E. Median

Solution Steps

The mean (average) of the heights recorded in the high-jump event is calculated using the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

where \( N \) is the number of data points and \( x_i \) are the individual heights. For our dataset, we have:

\[ \mu = \frac{939}{13} \approx 72.23 \]

To find the median, we first sort the data:

\[ \text{Sorted data} = [53, 57, 63, 63, 64, 64, 65, 67, 67, 72, 72, 73, 159] \]

The median is the value at the position given by the formula:

\[ \text{Rank} = Q \times (N + 1) = 0.5 \times (13 + 1) = 7.0 \]

Since the rank is 7, the median corresponds to the value at the 7th position in the sorted list, which is:

\[ \text{Median} = 65 \]

The mode is the value that appears most frequently in the dataset. From the sorted data, we can see that the value \( 63 \) appears most often. Therefore, the mode is:

\[ \text{Mode} = 63 \]

Final Answer