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Yasmine works as a server in a restaurant and earns different amounts in tips each night. Her median earnings in tips over the course of 8 nights of work is $39.50. Her minimum tip earnings were $10.45, and her maximum tip earnings were $96.78. What is a possible dataset of tip earnings?(1 point) Responses {$10.45,$20.50,$35.80,$38.10,$40.90,$45.90,$105.96,$96.78} left brace $10.45 comma $20.50 comma $35.80 comma $38.10 comma $40.90 comma $45.90 comma $105.96 comma $96.78 right brace {$10.45,$20.50,$35.80,$38.10,$40.90,$45.90,$79.60,$96.78} left brace $10.45 comma $20.50 comma $35.80 comma $38.10 comma $40.90 comma $45.90 comma $79.60 comma $96.78 right brace {$10.45,$39.50,$39.50,$78.10,$80.90,$95.90,$109.40,$110.80} left brace $10.45 comma $39.50 comma $39.50 comma $78.10 comma $80.90 comma $95.90 comma $109.40 comma $110.80 right brace {$10.45,$20.50,$35.80,$38.10,$39.50,$42.50,$45.90,$79.60,$96.78}

1 answer

To find a possible dataset of tip earnings for Yasmine that meets the given conditions, we need to ensure:

  1. The dataset contains 8 values.
  2. The minimum earnings is $10.45.
  3. The maximum earnings is $96.78.
  4. The median earnings is $39.50, which means that when the earnings are sorted, the average of the 4th and 5th values (since there are 8 values) should equal $39.50.

Given the responses, let's evaluate them based on these conditions.

  1. First option: {$10.45, $20.50, $35.80, $38.10, $40.90, $45.90, $105.96, $96.78}

    • This has 8 values.
    • The minimum is $10.45 and the maximum is $105.96 (which is outside the specified max of $96.78). This option is invalid.

  2. Second option: {$10.45, $20.50, $35.80, $38.10, $40.90, $45.90, $79.60, $96.78}

    • This has 8 values.
    • The minimum is $10.45 and the maximum is $96.78.
    • The sorted values are $10.45, $20.50, $35.80, $38.10, $40.90, $45.90, $79.60, $96.78.
    • The 4th and 5th values are $38.10 and $40.90; their average is (38.10 + 40.90)/2 = 39.50, which matches the median. This option is valid.

  3. Third option: {$10.45, $39.50, $39.50, $78.10, $80.90, $95.90, $109.40, $110.80}

    • This has 8 values.
    • The minimum is $10.45 but the maximum is $110.80 (which is outside the specified max of $96.78). This option is invalid.

  4. Fourth option: {$10.45, $20.50, $35.80, $38.10, $39.50, $42.50, $45.90, $79.60, $96.78}

    • This has 9 values and thus does not meet the requirement of 8 values. This option is invalid.

Based on the evaluation, the second option {$10.45, $20.50, $35.80, $38.10, $40.90, $45.90, $79.60, $96.78} is a valid dataset.