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Zorluk: Çok zorDescriptive Statistics Interpretation

The table below displays operational performance metrics for 10 regional cold-chain distribution centers operated by a pharmaceutical logistics company across two geographic zones.

Distribution CenterZoneCold Storage Volume (103 m310^3\text{ m}^3)Temperature ExcursionsOn-Time Delivery Rate (%)
Center H-1Zone East451294.2
Center H-2Zone West801891.5
Center H-3Zone East60896.8
Center H-4Zone East302289.0
Center H-5Zone West551493.4
Center H-6Zone East75598.1
Center H-7Zone West401692.0
Center H-8Zone East901195.5
Center H-9Zone West65995.0
Center H-10Zone East501592.6

By how many percentage points does the median On-Time Delivery Rate of the distribution centers in Zone East exceed the mean On-Time Delivery Rate of all 10 distribution centers?

  1. 1.04 percentage pointsCevap
  2. B
    0.39 percentage points
  3. C
    1.69 percentage points
  4. D
    0.56 percentage points
  5. E
    0.26 percentage points

Cevap

The median On-Time Delivery Rate of Zone East distribution centers exceeds the mean On-Time Delivery Rate of all 10 centers by 1.04 percentage points.
The mean of all 10 distribution centers is calculated by summing all on-time delivery rates (938.1%938.1\%) and dividing by 10 to get 93.81%93.81\%. Filtering for Zone East gives 6 centers with delivery rates [89.0%,92.6%,94.2%,95.5%,96.8%,98.1%][89.0\%, 92.6\%, 94.2\%, 95.5\%, 96.8\%, 98.1\%]. Because N=6N = 6 is even, the median is the average of the 3rd (94.2%94.2\%) and 4th (95.5%95.5\%) terms, yielding 94.85%94.85\%. Subtracting 93.81%93.81\% from 94.85%94.85\% gives 1.041.04 percentage points.

Adım Adım Çözüm

1
Calculate the mean On-Time Delivery Rate for all 10 distribution centers.
Sum of all delivery rates = 94.2+91.5+96.8+89.0+93.4+98.1+92.0+95.5+95.0+92.6=938.1%94.2 + 91.5 + 96.8 + 89.0 + 93.4 + 98.1 + 92.0 + 95.5 + 95.0 + 92.6 = 938.1\%. Mean = 938.110=93.81%\frac{938.1}{10} = 93.81\%.
To establish the overall average delivery performance benchmark across all facilities.
2
Filter the dataset to isolate the distribution centers in Zone East.
Zone East consists of 6 centers: H-1 (94.2%94.2\%), H-3 (96.8%96.8\%), H-4 (89.0%89.0\%), H-6 (98.1%98.1\%), H-8 (95.5%95.5\%), and H-10 (92.6%92.6\%).
The question specifically requires evaluating the median of the Zone East subset.
3
Sort the Zone East On-Time Delivery Rates in ascending order.
Sorted list of 6 values: [89.0%,92.6%,94.2%,95.5%,96.8%,98.1%][89.0\%, 92.6\%, 94.2\%, 95.5\%, 96.8\%, 98.1\%].
Sorting is a mandatory prerequisite step before determining the median of any dataset.
4
Calculate the median of the even-count (N = 6) Zone East subset.
The two central values (3rd and 4th) are 94.2%94.2\% and 95.5%95.5\%. Median = 94.2+95.52=94.85%\frac{94.2 + 95.5}{2} = 94.85\%.
For an even number of elements, the median is defined as the exact arithmetic mean of the two middle elements.
5
Compute the difference between the calculated median and mean.
94.85%−93.81%=1.0494.85\% - 93.81\% = 1.04 percentage points.
To answer the specific target question regarding the margin by which the median exceeds the mean.

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