1. **State the problem:** We have two data sets, A and B. Data set A has 21 values including one outlier 19, and data set B is data set A without the outlier 19, so it has 20 values. We want to compare the medians of data sets A and B. 2. **Recall the median definition:** The median is the middle value when data are ordered. For an odd number of values $n$, median is the value at position $\frac{n+1}{2}$. For an even number $n$, median is the average of values at positions $\frac{n}{2}$ and $\frac{n}{2}+1$. 3. **List data set A values with frequencies:** - 0 appears 1 time - 1 appears 3 times - 2 appears 4 times - 3 appears 5 times - 4 appears 4 times - 5 appears 3 times - 19 appears 1 time Total values: $1+3+4+5+4+3+1=21$ 4. **Find median position for data set A:** Since $n=21$ (odd), median position is $\frac{21+1}{2}=11$th value. 5. **Locate 11th value in ordered data set A:** Cumulative counts: - 0: 1 value (positions 1) - 1: 3 values (positions 2-4) - 2: 4 values (positions 5-8) - 3: 5 values (positions 9-13) The 11th value lies in the 3's group (positions 9 to 13), so median of A is 3. 6. **Create data set B by removing 19:** Now total values $=21-1=20$ (even). 7. **Find median positions for data set B:** Median is average of values at positions $\frac{20}{2}=10$ and $10+1=11$. 8. **Locate 10th and 11th values in data set B:** Cumulative counts without 19: - 0: 1 (pos 1) - 1: 3 (pos 2-4) - 2: 4 (pos 5-8) - 3: 5 (pos 9-13) Positions 10 and 11 are both in the 3's group. 9. **Calculate median of B:** Median is average of 3 and 3, which is 3. 10. **Compare medians:** Median of A = 3, median of B = 3, so they are equal. **Final answer:** (B) The median of data set B is equal to the median of data set A.