Determine the following data’s mean, median, and mode: 12, 13, 16, 43, 13, 13, 16, 17, 19, 21, 22, 34, 54, 42, 3, 4, 8, 10, 12.
Compute mean, median and mode for the following data : 12, 13, 16, 43, 13, 13, 16, 17, 19, 21, 22, 34, 54, 42, 3, 4, 8, 10, 12.
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1. Introduction
Calculating the mean, median, and mode is a fundamental aspect of descriptive statistics, providing insights into the central tendency and distribution of data. In this case, we will compute the mean, median, and mode for the given dataset: 12, 13, 16, 43, 13, 13, 16, 17, 19, 21, 22, 34, 54, 42, 3, 4, 8, 10, 12.
2. Mean Calculation
The mean, also known as the average, is calculated by summing all the values in the dataset and dividing by the total number of values.
Mean = (12 + 13 + 16 + 43 + 13 + 13 + 16 + 17 + 19 + 21 + 22 + 34 + 54 + 42 + 3 + 4 + 8 + 10 + 12) / 19
Mean = 393 / 19
Mean ≈ 20.68
3. Median Calculation
The median is the middle value of the dataset when arranged in ascending order. If there is an odd number of values, the median is the middle value. If there is an even number of values, the median is the average of the two middle values.
First, let's arrange the data in ascending order:
3, 4, 8, 10, 12, 12, 13, 13, 13, 16, 16, 17, 19, 21, 22, 34, 42, 43, 54
Since there are 19 values (odd), the median is the 10th value, which is 16.
4. Mode Calculation
The mode is the value that appears most frequently in the dataset.
From the dataset:
Therefore, the mode of the dataset is 13, as it appears most frequently.
5. Conclusion
In summary, for the given dataset:
These descriptive statistics provide insights into the central tendency and distribution of the data. The mean indicates the average value, the median represents the middle value, and the mode indicates the most frequently occurring value. These measures help summarize the dataset and provide a better understanding of its characteristics.