Yasmine works as a server at a restaurant and earns different amounts in tips each night. Her tip earnings for her past 7 nights of work are listed below: $35.80, $79.60, $38.10, $20.50, $10.45, $96.78, $45.90 Yasmine calculates that her mean tip earnings is $46.73, and her median tip earnings is $38.10. If Yasmine makes $25.32 in tips the next time she works, how will the values of her mean and median tip earnings change? Round all answers to two decimal places.(1 point)

1 answer

To determine how Yasmine's mean and median tip earnings will change after she makes an additional $25.32, we'll first update her total earnings and then recalculate the mean and median.

Current Earnings:

  • Night 1: $35.80
  • Night 2: $79.60
  • Night 3: $38.10
  • Night 4: $20.50
  • Night 5: $10.45
  • Night 6: $96.78
  • Night 7: $45.90

Current Statistics:

  • Total Earnings: \( 35.80 + 79.60 + 38.10 + 20.50 + 10.45 + 96.78 + 45.90 = 326.13 \)
  • Number of Nights: 7
  • Mean Tip Earnings: \( \text{Mean} = \frac{326.13}{7} \approx 46.73 \) (confirmed)
  • Median Tip Earnings: The sorted earnings are:
    • $10.45, $20.50, $35.80, $38.10, $45.90, $79.60, $96.78
    • Since there are 7 values, the median is the 4th value, which is $38.10 (confirmed).

Update for the 8th Night:

Yasmine earns $25.32 in tips next:

  • New Total Earnings: \[ 326.13 + 25.32 = 351.45 \]
  • New Number of Nights: \[ 7 + 1 = 8 \]

New Mean:

  • Calculate the new mean: \[ \text{New Mean} = \frac{351.45}{8} \approx 43.93 \]

New Median:

  • New Earnings List (including the new tip):
    • $10.45, $20.50, $25.32, $35.80, $38.10, $45.90, $79.60, $96.78
  • Sorted list:
    • $10.45, $20.50, $25.32, $35.80, $38.10, $45.90, $79.60, $96.78
  • Since there are 8 values, the median will be the average of the 4th and 5th numbers: \[ \text{New Median} = \frac{35.80 + 38.10}{2} = \frac{73.90}{2} = 36.95 \]

Summary:

  • New Mean: \( 43.93 \)
  • New Median: \( 36.95 \)

Thus, after earning an additional $25.32, Yasmine's new mean tip earnings is approximately $43.93 and her new median tip earnings is approximately $36.95.