To find the mean (average), you total all the numbers and then divide by the count of numbers. For the given data set:
Mean = (3 + 24 + 28 + 29 + 26 + 29) / 6
Mean = (139) / 6
Mean ≈ 23.17
To find the median (the middle value when the data is ordered), you would first order the data and then pick the middle value or the average of the two middle numbers (if the data set has an even number of observations). In your case, the data set is already in ascending order:
Ordered data set: 3, 24, 26, 28, 29, 29
Since there are six numbers, we take the average of the two middle numbers, which are 26 and 28.
Median = (26 + 28) / 2
Median = 54 / 2
Median = 27
The mode is the number that appears most frequently. In the given data set:
Mode = 29 (since it appears twice, more than any other number)
Now, to decide which measure best describes the data, let's consider what each measure tells us:
1. Mean: It is sensitive to extreme values or outliers. In this data set, the number 3 is quite low compared to the other numbers and might be pulling the mean down.
2. Median: It is robust to outliers and gives a better sense of the middle point of the data without being skewed by extreme values. Hence, it might be considered a more accurate representation of the central tendency for this dataset.
3. Mode: It is the most frequent value in the data set. Since the mode is at the higher end of the data and only relevant to frequency (and not necessarily the center of the data), it may not best describe the central tendency for the entire data set.
In conclusion, the median would likely be the best descriptor of central tendency for this data set because it is less affected by the low value (outlier) and sits comfortably in the middle of the ordered data.
Find the mean, median, and mode for the data set below. Explain which measure best describes the data.
3 24 28 29 26 29
1 answer