The median rainfall during a spring storm in the lowlands is about 4 mm less than a spring storm in the highlands. The mean rainfall for the lowlands is about 3 mm less than for the highlands. Why is there a difference in the central measures for each data set?
The mean and the median are different because the data for the highlands has more variation than the data for the lowlands. The mean is affected by the outliers in the lowlands data.
The mean and the median are different because the data for the highlands has more variation than the data for the lowlands. The mean is affected by the outliers in the lowlands data.
Mean and median will differ when there is variation or spread in the distribution.
The rainfall for the lowlands had possible outliers and , therefore, a higher variation.
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The difference in the central measures, specifically the median and the mean, between the lowlands and highlands can be attributed to the distribution of rainfall values within each dataset.
To understand the difference, let's first define the median and mean:
1. Median: The median represents the middle value when the data is arranged in ascending or descending order. It is not impacted by extreme values and is an indicator of the central tendency without considering the actual values.
2. Mean: The mean is the average of all values in the dataset. It takes into account every value equally and can be influenced by extreme values.
Now, let's consider the explanation for the difference in the central measures between the lowlands and highlands:
1. Median: The fact that the median rainfall during a spring storm in the lowlands is about 4 mm less than in the highlands indicates that, on average, there are more rainfall values above the median in the highlands as compared to the lowlands. In other words, the distribution of rainfall values in the highlands extends further towards higher values. As a result, the median for the highlands is higher than for the lowlands.
2. Mean: The mean rainfall for the lowlands being about 3 mm less than the mean for the highlands suggests that the overall average rainfall value in the highlands is significantly influenced by extreme values that are larger. Therefore, the highlands have a higher mean due to those larger values, which effectively pulls the average upwards. Conversely, in the lowlands, either due to fewer extreme values or lower individual rainfall amounts, the mean is lower.
In summary, the difference in central measures indicates that the distribution of rainfall values in the highlands is skewed towards higher values, affecting both the median and mean. Conversely, the lowlands experience less extreme values, resulting in a lower median and mean rainfall.
mean means average, sum over number of sprinkles/ number.
Median means half the sprinkles were higher and half lower.
If most sprinkles were sprinkles and one was a hurricane, the median would be about in the middle but the average would be pulled way up by the big rainstorm.