A sales manager has sampled past sales records to determine how many air conditioners are sold each day. Daily records for a sample of 10 days have been selected. The sales on these days are: 0, 2, 6, 9, 10, 7, 5, 0, 4, 5. The 75th percentiles of daily sales is _________

Question

BlackTom AI · Accepted Answer

Percentiles partition ordered data; the 75th percentile is the value at or above which 75% of the observations lie. Relevant knowledge: percentiles require the data to be ordered and then a rule (rank formula) is used to pick the percentile value. A commonly used classroom rule for discrete samples (the "nearest-rank" method) finds the rank r = ceil(P/100 * n) and takes the observation at that rank.

Step-by-step reasoning and calculations:
1. Order the sample (n = 10) from smallest to largest.
   Original data: 0, 2, 6, 9, 10, 7, 5, 0, 4, 5
   Ordered data: 0, 0, 2, 4, 5, 5, 6, 7, 9, 10
   Positions 1 through 10 correspond to these values.
2. Compute the rank using the nearest-rank method:
   r = ceil(0.75 * 10) = ceil(7.5) = 8
3. The 8th ordered observation is 7 (see ordered list).
   Therefore, the 75th percentile (by nearest-rank) = 7.

Intermediate calculations shown: 0.75 * 10 = 7.5; ceil(7.5) = 8; value at position 8 = 7.

Why this answer is correct: The multiple-choice context implies the nearest-rank definition (no interpolation) is intended; under that standard procedure the 75th percentile is the 8th smallest value, which is 7.

Why other options are incorrect:
- 2 corresponds to the 3rd ordered value (far below the 75th percentile).
- 5 is the 5th and 6th ordered values (below the 75th percentile).
- 10 is the maximum (10th value), which would be the 100th percentile, not the 75th.

Conclusion: Using the nearest-rank method on the ordered sample yields 7 as the 75th percentile, matching the provided correct answer 7.

A sales manager has sampled past sales records to determine how many air conditioners are sold each day. Daily records for a sample of 10 days have been selected. The sales on these days are: 0, 2, 6, 9, 10, 7, 5, 0, 4, 5. The 75th percentiles of daily sales is _________单项选择题

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