To calculate the mean, median, and mode of the given data set, let's first organize the information and proceed step by step.

Data:

23, 18, 24, 23, 31, 37, 28, 30, 25, 40, 35, 35, 27, 25

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1. Mean:

The mean is the average of all the numbers. To find it, we sum all the numbers and divide by the total number of values.

Steps:

1. Add all the numbers: $23 + 18 + 24 + 23 + 31 + 37 + 28 + 30 + 25 + 40 + 35 + 35 + 27 + 25 = 402$

2. Count the total number of data points: There are 14 values.

3. Calculate the mean: $\text{Mean} = \frac{402}{14} = 28.71 \, (\text{rounded to two decimal places})$

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2. Median:

The median is the middle value when the data is ordered in increasing or decreasing order. If the number of data points is odd, it is the middle value; if even, it is the average of the two middle values.

Steps:

1. Sort the data in increasing order: $18, 23, 23, 24, 25, 25, 27, 28, 30, 31, 35, 35, 37, 40$

2. Since there are 14 values (even), the median will be the average of the 7th and 8th numbers in the sorted list. The 7th value is 27, and the 8th value is 28.

3. Calculate the median: $\text{Median} = \frac{27 + 28}{2} = 27.5$

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3. Mode:

The mode is the number that occurs most frequently in the data.

Steps:

• From the sorted data: $18, 23, 23, 24, 25, 25, 27, 28, 30, 31, 35, 35, 37, 40$
• The numbers that repeat are 23, 25, and 35, each appearing twice.

Since there are multiple values that appear the most, the data set is multimodal.

Conclusion:

• Mean = 28.71
• Median = 27.5
• Mode = 23, 25, 35 (multimodal)

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Would you like further details or have any questions about this? Here are some related questions you might find helpful:

1. How do you find the mean, median, and mode for large data sets?
2. What happens if there is no mode in a data set?
3. Can the mean be used when the data set has outliers?
4. How do you calculate the range and standard deviation of data?
5. Why does the median work better than the mean when there are extreme outliers?

Tip: Always sort the data before calculating the median or mode to avoid mistakes and ensure accuracy.