Using Empirical Formula Calculate the Mode of the Following Data: 17, 16, 25, 23, 22, 23, 28, 25, 25, 23. 

Answer: The mode of the given data (17, 16, 25, 23, 22, 23, 28, 25, 25, 23) is 23.6, which corresponds to option C. 23.6 . In statistics, the mode is the most frequently occurring number in a given dataset. It represents the value that appears most often.

Complete Answer:

Step 1: Arrange the Data in Ascending Order

Given data: 17, 16, 25, 23, 22, 23, 28, 25, 25, 23

Arranging in order:
16, 17, 22, 23, 23, 23, 25, 25, 25, 28

Step 2: Find the Mean

The mean (average) is calculated as:

Mean = Sum of all values Total number of values \text{Mean} = \frac{\text{Sum of all values}}{\text{Total number of values}}    

  = 16 + 17 + 22 + 23 + 23 + 23 + 25 + 25 + 25 + 28 10 = \frac{16 + 17 + 22 + 23 + 23 + 23 + 25 + 25 + 25 + 28}{10}    

   = 227 10 = 22.7 = \frac{227}{10} = 22.7    

Step 3: Find the Median

The median is the middle value of an ordered dataset.

Since there are 10 numbers, the median is the average of the 5th and 6th values:

Median = 23 + 23 2 = 46 2 = 23 \text{Median} = \frac{23 + 23}{2} = \frac{46}{2} = 23    

Step 4: Apply the Empirical Formula

Mode = 3 × Median − 2 × Mean \text{Mode} = 3 \times \text{Median} – 2 \times \text{Mean}    

  = 3 × 23 − 2 × 22.7 = 3 \times 23 – 2 \times 22.7    

= 69 − 45.4 = 69 – 45.4    

= 23.6 = 23.6    

Thus, the correct answer is 23.6 (Option C).

Fun Fact 

Did you know that in some cases, data can have no mode, one mode (unimodal), or multiple modes (bimodal or multimodal)? When no value repeats, we say the dataset is mode-less!

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