A random sample of 12 joggers was asked to keep track and report the number of miles they ran last week. The responses are:
5.5 7.2 1.6 22.0 8.7 2.8 5.3 3.4 12.5 18.6 8.3 6.6
Compute the three statistics that measure central location
To compute the three statistics that measure central location (also known as measures of central tendency) for the given data set, you would need to calculate the mean, median, and mode.
1. Mean: The mean is calculated by summing up all the values in the data set and dividing the sum by the number of values. To find the mean for the given sample, you would add up all the reported miles and divide by 12.
Mean = (5.5 + 7.2 + 1.6 + 22.0 + 8.7 + 2.8 + 5.3 + 3.4 + 12.5 + 18.6 + 8.3 + 6.6) / 12
2. Median: The median is the middle value of a sorted data set. To find the median, you first need to sort the data set in ascending order. In this case, the sorted list of miles would be:
1.6, 2.8, 3.4, 5.3, 5.5, 6.6, 7.2, 8.3, 8.7, 12.5, 18.6, 22.0
Since the sample size is even (12), there are two middle values: 6.6 and 7.2. To find the median, you calculate the average of these two values:
Median = (6.6 + 7.2) / 2
3. Mode: The mode is the value(s) that appears most frequently in the data set. In this case, there is no value that appears more than once, so the data set has no mode.
Therefore, the three statistics that measure central location for the given data set are:
- Mean: Calculated by adding up all reported miles and dividing by 12.
- Median: Calculated by taking the average of the middle two values of the sorted list.
- Mode: Not applicable as there is no value that appears more than once.
Follow the guidelines here:
http://math.about.com/od/statistics/a/MeanMedian.htm
The three statistics they have in mind are probably median, mean and mode.
In this case, there is no mode, since no number appears more than once.You might tell them what the range is, instead of the mode.
The mean and median are easily computed.