Question

julian and nina are playing a game. their scores for five games are shown in the table below. 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 medians differ by 3, but the ranges differ by 2. the medians differ by 1, but the ranges differ by 10. the means differ by 1, 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. Since there are \(5\) values, 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. Since there are \(5\) values, the median \(m_N = 45\).
The range \(R_N=\text{Max}-\text{Min}=49 - 27 = 22\).

Step3: Calculate the difference in medians and ranges

Median difference: \(|m_N - m_J|=|45 - 42| = 3\).
Range difference: \(|R_N - R_J|=|22 - 12|=10\).

Answer:

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