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
a) Compare the three statistics that measure central location.
b) Briefly describe what each statistic tells you.
calculate
Can you calculate the mean, mode and median?
a) The three statistics that measure central location are the mean, median, and mode.
b) The mean is calculated by summing up all the values and dividing by the number of values. It represents the average value of the data set and is affected by extreme values.
The median is the middle value of the data set when arranged in ascending order. If there are two middle values, the median is the average of those two values. It represents the value that separates the highest and lowest values, and is not affected by extreme values.
The mode is the value(s) that appear most frequently in the data set. It represents the most common value(s) and can be used to determine the peak of the data's distribution. Unlike the mean and median, the mode can be applied to both numerical and categorical data.
To compare three statistics that measure central location (measures of central tendency) for the given data, we need to calculate the mean, median, and mode.
a) The three statistics are:
1) Mean: It is calculated by summing up all the values and dividing it by the total number of values.
2) Median: It is the middle value in a dataset when arranged in ascending order. If there is an even number of values, it is the average of the two middle values.
3) Mode: It is the value that appears most frequently in a dataset.
b) The meanings of each statistic:
1) Mean: The mean provides an average value that represents the typical value or central value of the dataset. It takes into account all the values in the dataset and is affected by outliers.
2) Median: The median represents the middle value in the dataset, which separates the dataset into two equal halves. It is not influenced by extreme values and provides a robust measure of central location.
3) Mode: The mode represents the most frequently occurring value in the dataset. It helps identify the value that is most common or popular among the data points.
Now, let's calculate these statistics for the given data:
1) Calculating Mean:
Sum of the values = 5.5 + 7.2 + 1.6 + 22.0 + 8.7 + 2.8 + 5.3 + 3.4 + 12.5 + 18.6 + 8.3 + 6.6 = 102.5
Mean = Sum of values / Total number of values = 102.5 / 12 = 8.54
2) Calculating Median:
Arranging the values in ascending order: 1.6, 2.8, 3.4, 5.3, 5.5, 6.6, 7.2, 8.3, 8.7, 12.5, 18.6, 22.0
Median = (5.3 + 6.6) / 2 = 6.95
3) Calculating Mode:
There is no repeated value in the dataset, so there is no mode.
Therefore, the three statistics that measure central location are:
Mean = 8.54
Median = 6.95
Mode = None (since there are no repeated values)
Remember, the mean provides an average value, the median represents the middle value or central tendency when ordered, and the mode identifies the most frequently occurring value.