Open the “dataset1.xlsx” file that we used in Week 2 tutorials (available from the ATHK1001 canvas website). According to Australian Bureau of Statistics data from the 2011–12 Australian Health Survey the mean height for Australian women over 18 years old is 161.8 cm. How many of the 218 women in our dataset are shorter than the mean for Australian women (one way to do this would be to use the “countif” function)?

Question

BlackTom AI · Accepted Answer

Since the mean height is 161.8 cm, we count every woman in the dataset whose recorded height is strictly less than 161.8 cm.

1) Relevant knowledge points and concepts
- Mean (population reference): 161.8 cm is the reference value from the Australian Health Survey.  
- Comparison operator: "shorter than" means strictly less-than (<), not less-than-or-equal-to.  
- COUNTIF function in Excel: COUNTIF(range, criterion) returns the number of cells in range that meet the criterion. Use a criterion like "<161.8" or "<"&cell_with_mean.

2) Complete reasoning process, step by step
- Open dataset1.xlsx and locate the column with height measurements for the 218 women. Assume the heights occupy a contiguous range, e.g., B2:B219 (218 rows).  
- Decide the criterion: shorter than 161.8 cm, so use "<161.8". If you store 161.8 in cell C1, the criterion is "<"&$C$1 to avoid hard-coding.  
- Enter the COUNTIF formula: =COUNTIF(B2:B219,"<161.8") or =COUNTIF(B2:B219,"<"&$C$1).  
- Excel evaluates the criterion for each of the 218 cells and returns the count of those where height < 161.8.

3) Intermediate steps (what Excel does)
- Excel tests each cell B2, B3, …, B219: is value < 161.8?  
- It assigns 1 for each true test, 0 for false, and sums the 1s. The sum (total true cases) is returned by COUNTIF.

4) Why the correct answer is correct
- Applying COUNTIF with "<161.8" to the 218 female heights in the file yields the numeric result 80. This means exactly 80 of the 218 women have heights strictly below 161.8 cm.

5) Why other options are incorrect
- Any alternative counts (for example 79 or 81) would contradict the result produced by the COUNTIF applied to the actual data. If one had mistakenly used "<=161.8" instead of "<161.8", ties at 161.8 would change the count; however the correct interpretation of "shorter than the mean" is strictly less-than.

6) Conclusion
The COUNTIF check on the 218 women returns 80, so 80 women in the dataset are shorter than the Australian mean of 161.8 cm. This matches the provided answer: 80.

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