Elephants consume an immense amount of water. A random sample of elephants' water consumption was tracked and the results of the R output for descriptive statistics are below. What is the inter-quartile range of this data? Round to the nearest hundredth.

summary(water)
Min. 1st Qu. Median Mean 3rd Qu. Max.
33.00 48.00 55.00 57.71 64.00 89.00

sd(water)
[1] 13.89588

length(water)
[1] 17

Question

Elephants consume an immense amount of water. A random sample of elephants' water consumption was tracked and the results of the R output for descriptive statistics are below. What is the inter-quartile range of this data? Round to the nearest hundredth.

summary(water)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  33.00   48.00   55.00   57.71   64.00   89.00

> sd(water)
[1] 13.89588
> 
> length(water)
[1] 17
>

BlackTom AI · Accepted Answer

Interquartile range (IQR) is defined as Q3 − Q1, where Q1 is the first quartile (25th percentile) and Q3 is the third quartile (75th percentile).

Relevant knowledge points:
- Quartiles divide ordered data into four equal parts: Q1 is the 25th percentile, the median is the 50th percentile, and Q3 is the 75th percentile.
- The IQR measures the spread of the middle 50% of the data and is computed as Q3 − Q1.
- The R summary() output directly reports these quartile values.

Step-by-step reasoning using the provided R output:
1. Read the summary(water) output:
   - 1st Qu. (Q1) = 48.00
   - 3rd Qu. (Q3) = 64.00
2. Compute the IQR by subtracting Q1 from Q3:
   - IQR = Q3 − Q1 = 64.00 − 48.00
3. Perform the subtraction:
   - 64.00 − 48.00 = 16.00
4. Round to the nearest hundredth (two decimal places):
   - 16.00 is already at the hundredth precision.

Why this is correct:
- The summary output gives the exact quartile values computed by R for the sample; using these values directly yields the IQR. This is the standard and correct procedure.

Why other common numbers would be incorrect:
- The sample mean (57.71) is a measure of center, not spread, so it is not the IQR.
- The sample standard deviation (≈13.89588) measures average deviation from the mean, not the middle 50% spread, so it is not the IQR.
- The range (Max − Min = 89 − 33 = 56) measures total spread, not IQR.

Conclusion:
The interquartile range is 16.00, which matches the provided correct answer.

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