2. Lizelle ran the following times for the last 7 half-marathons she entered: \( 2 \mathrm{~h}: 00 \mathrm{~min} 2 \mathrm{~h}: 05 \mathrm{~min} 2 \mathrm{~h}: 00 \mathrm{~min} 2 \mathrm{~h}: 00 \mathrm{~min} \quad 1 \mathrm{~h}: 58 \mathrm{~min} 2 \mathrm{~h}: 01 \mathrm{~min} 2 \mathrm{~h}: 45 \mathrm{~min} \) 2.1 What is the mean of her race times? [HINT! Convert data into minutes] 2.2 What is the median of her race times? 2.3 What is the mode of her race times? 2.4 Which measure of central tendency is a better indication of her time for a half-marathon? Explain your answer. 2.5 \( \begin{array}{l}\text { Her time of } 2 \mathrm{~h}: 45 \text { min seems to be out of the ordinary when compared with her } \\ \text { other running times. Suggest possible reasons for this running time. }\end{array} \)

To calculate the averages and trends in Lizelle's running times, let's first convert everything into minutes for easier calculations. For the mean, we first convert: - 2h 00min = 120 min - 2h 05min = 125 min - 2h 00min = 120 min - 2h 00min = 120 min - 1h 58min = 118 min - 2h 01min = 121 min - 2h 45min = 165 min Now, calculating the mean: \[ \text{Mean} = \frac{120 + 125 + 120 + 120 + 118 + 121 + 165}{7} = \frac{ 1, 1 0}{7} \approx 1 6 .1 4 \, \text{min} \] So, the mean time is approximately **2h 16min**. For the median, we first arrange her times: - 1h 58min (118 min) - 2h 00min (120 min) - 2h 00min (120 min) - 2h 00min (120 min) - 2h 01min (121 min) - 2h 05min (125 min) - 2h 45min (165 min) The middle value (4th in a sorted list of 7) is **2h 00min (120 min)**, so the median is **2h 00min**. The mode is the most frequently occurring time, and looking at the list, **2h 00min (120 min)** occurs **three times**, making it the mode. For the best representation of Lizelle's running abilities, the **median** is often more informative in this case since the outlier (2h 45min) skews the mean upwards. This provides a better indication of her typical performance, especially when performances vary widely. Regarding the outlier time of **2h 45min**, there can be several factors. Perhaps Lizelle faced adverse weather conditions, an injury, or simply had an off day due to fatigue. Maybe there was a fun distraction or even some technical problem with her gear. Life happens, and even the best athletes can have days that don’t reflect their true potential!