Find the mean, median, and mode for the data set below. Explain which measure best describes the data.
3 27 22 23 25 22
To find the mean, median, and mode for this data set, we need to carry out a few calculations:
**Mean:**
The mean is the average of all the numbers. To find it, you sum up all the numbers and then divide by the total count of the numbers.
Mean = (3 + 27 + 22 + 23 + 25 + 22) / 6
Mean = 122 / 6
Mean = 20.33 (rounded to two decimal places)
**Median:**
The median is the middle number in a data set that has been arranged in ascending or descending order. If there is an even number of observations, the median is the average of the two middle numbers.
First, arrange the data in ascending order:
3, 22, 22, 23, 25, 27
As there are six numbers, we will take the average of the third and fourth number to find the median:
Median = (22 + 23) / 2
Median = 45 / 2
Median = 22.5
**Mode:**
The mode is the number that appears most often in the data set.
Looking at the data set, we can see that 22 is the only number that repeats:
3, 22, 22, 23, 25, 27
So, the mode is 22.
**Which measure best describes the data?**
- The mean can be affected by outliers or data that is not symmetrically distributed. In this case, the value '3' is much lower than the others and could be an outlier.
- The median is less affected by outliers and skewed data, and it gives us the middle point of the dataset.
- The mode is the most frequent number in the set, giving us an idea about the most common value.
Looking at the data set, since we have an outlier (the value '3'), the mean might not be the best representation of the typical value in this data set, as it's likely dragged down by that low value. The median, which isn't pulled by extreme values, could be a better measure of the center for this data set, as it falls near the middle of the other values. The mode tells us the most common value, but in this case, we only have a repeat of one number, which doesn't provide a lot of information about the central tendency of the dataset.
In conclusion, the median might be the most representative measure of central tendency for this particular set of data because it is less affected by the outlier and shows the central value when the data is ordered by size.