a. Find the mean, median, and mode of the numbers: 12, 9, 17, 15, 10. – Mean: – Median: – Mode:
The Correct Answer and Explanation is:
To calculate the mean, median, and mode of the numbers 12, 9, 17, 15, and 10, let’s follow the steps for each measure of central tendency.
1. Mean:
The mean is calculated by adding all the numbers together and dividing by the total count of numbers.
Step 1: Add the numbers:
[
12 + 9 + 17 + 15 + 10 = 63
]
Step 2: Count the numbers:
There are 5 numbers in total.
Step 3: Divide the sum by the count:
[
\text{Mean} = \frac{63}{5} = 12.6
]
2. Median:
The median is the middle value when the numbers are arranged in ascending order.
Step 1: Arrange the numbers in ascending order:
[
9, 10, 12, 15, 17
]
Step 2: Since there are 5 numbers (an odd count), the median is the middle number:
The middle number is the third one:
[
\text{Median} = 12
]
3. Mode:
The mode is the number that appears most frequently in a data set.
In the set 12, 9, 17, 15, and 10, all numbers appear only once. Since no number repeats, this data set does not have a mode:
[
\text{Mode} = \text{None}
]
Summary of Results:
- Mean: 12.6
- Median: 12
- Mode: None
Explanation:
Understanding the mean, median, and mode is crucial for analyzing data sets. The mean provides an average value, offering a quick snapshot of the overall trend in the data. It is sensitive to extreme values, known as outliers, which can skew the average significantly. For instance, if we added a very high number to our data set, the mean would increase.
The median, however, remains unaffected by outliers and gives a better representation of the center value in a skewed distribution. This is particularly useful in real-world scenarios like income levels where a few high incomes can distort the mean.
The mode highlights the most common value within the data set. In this case, having no mode indicates a diverse set of values without repetition, which could imply varied responses or characteristics in the context of the data being analyzed. Understanding these concepts aids in making informed decisions based on statistical data.