Question

julian and nina are playing a game. their scores for five games are shown in the table. julians and ninas scores julians scores 42 41 46 50 38 ninas scores 47 27 45 32 49 which statement comparing the medians to the ranges is true? the medians differ by 3, but the ranges differ by 10. the means differ by 1, but the ranges differ by 2. the medians differ by 1, but the ranges differ by 10. the medians differ by 3, but the ranges differ by 2.

Explanation:

Step1: Sort Julian's scores

Sort Julian's scores: \(38,41,42,46,50\). The median is the middle value. For \(n = 5\) (odd number of data points), the median \(M_J=42\). The range \(R_J=\text{Max}-\text{Min}=50 - 38=12\).

Step2: Sort Nina's scores

Sort Nina's scores: \(27,32,45,47,49\). The median is the middle value. For \(n = 5\) (odd number of data points), the median \(M_N = 45\). The range \(R_N=\text{Max}-\text{Min}=49 - 27 = 22\).

Step3: Calculate the difference in medians and ranges

The difference in medians: \(|M_N - M_J|=|45 - 42| = 3\). The difference in ranges: \(|R_N - R_J|=|22 - 12|=10\).

Answer:

The medians differ by 3, but the ranges differ by 10.