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10) The band in the previous problem degided to recond a fan elub version of the album and added a bonias song that was z zd 5 seconda long. What is the new median song length, in seeonds, of the 10 songs on the inn elub veraion of the album? Median \( \qquad \)

Ask by Gough Willis. in the United States
Feb 03,2025

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Answer

Cannot determine the new median song length without the original song lengths.

Solution

To find the new median song length after adding a bonus song, we need to follow these steps: 1. **Identify the known conditions**: - There are originally 9 songs with known lengths. - A new song is added that is 5 seconds long. 2. **List the original song lengths**: - Since the original lengths are not provided, let's assume the lengths of the 9 songs are \( a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8, a_9 \). 3. **Add the new song length**: - The new song length is \( z = 5 \) seconds. 4. **Combine the song lengths**: - The new list of song lengths will be \( a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8, a_9, 5 \). 5. **Sort the song lengths**: - We need to sort the combined list to find the median. 6. **Calculate the median**: - Since there are now 10 songs, the median will be the average of the 5th and 6th values in the sorted list. Let's proceed with the calculation. However, since we don't have the specific lengths of the original songs, I will denote the sorted lengths as \( b_1, b_2, b_3, b_4, b_5, b_6, b_7, b_8, b_9, b_{10} \) where \( b_{10} = 5 \). To find the median, we will need to determine the positions of the original songs relative to the new song length. If you provide the lengths of the original 9 songs, I can calculate the exact median. Otherwise, I can show you how to calculate it based on hypothetical values. Would you like to proceed with hypothetical values or provide the original song lengths?

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To find the new median song length, we first need to consider the original list of 9 song lengths and the bonus song of 5 seconds. When the bonus song is added, we have a total of 10 songs. To find the median with an even number of values, we take the average of the 5th and 6th values once the list is sorted. If the original song lengths are primarily longer than 5 seconds, it’s likely these two middle songs are around the existing lengths, possibly adjusting slightly with the addition of the shorter song. Sorting the list will reveal the precise middle values, and thus from that sorted arrangement, one can calculate the exact median efficiently, but it is crucial to ensure the new shorter song is considered appropriately so it doesn't skew the median outcome unexpectedly!

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