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.
calculation
mean= 8.541
median= 6.9
Mean: 8.54; Median: 6.9; Mode: All
To find the three statistics that measure central location for the given data set, we need to calculate the mean, median, and mode. Here are the calculations:
a) Comparing the three statistics that measure central location:
Mean: Sum up all the data points and divide by the number of data points.
Sum of all the data points = 5.5 + 7.2 + 1.6 + 22.0 + 8.7 + 2.8 + 5.3 + 3.4 + 12.5 + 18.6 + 8.3 + 6.6 = 101.5
Number of data points = 12
Mean = Sum of all the data points / Number of data points = 101.5 / 12 ≈ 8.4583
Median: Arrange the data points in ascending order and find the middle value.
Arranged data points 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 = (5.5 + 6.6) / 2 = 6.05
Mode: Find the value(s) that appear most frequently in the data set.
There is no value that appears more than once in the given data set, so there is no mode.
b) Briefly describing what each statistic tells us:
Mean: The mean tells us the average number of miles run by the joggers last week. It is calculated by summing up all the data points and dividing by the number of data points. In this case, the mean is approximately 8.4583.
Median: The median tells us the middle value of the data set when arranged in ascending order. It provides a measure of the central location that is less influenced by extreme values. In this case, the median is 6.05.
Mode: The mode tells us the most frequently occurring value(s) in the data set. It provides insight into the most common mileage reported by the joggers. In this case, there is no mode as no value appears more than once.
To compare the three statistics that measure central location, we need to calculate the mean, median, and mode of the given data set.
a) Calculation of central location statistics:
Mean (Average) = (Sum of all values) / (Number of values)
Median = Middle value when the data set is arranged in ascending order
Mode = The value that appears most frequently in the data set
Given data set: 5.5, 7.2, 1.6, 22.0, 8.7, 2.8, 5.3, 3.4, 12.5, 18.6, 8.3, 6.6
1. Mean (Average):
Sum of all 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
Number of values = 12
Mean = 102.5 / 12 ≈ 8.54
2. Median:
Arranging the data set 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
Since the data set has an even number of values, the median is the average of the two middle values:
Median = (5.5 + 6.6) / 2 = 12.1 / 2 = 6.05
3. Mode:
No value in the data set appears more than once, so there is no mode.
b) Interpretation of the central location statistics:
Mean (Average) - The mean gives the average value of the data set. In this case, the mean mileage ran by the joggers last week is approximately 8.54 miles.
Median - The median represents the middle value of the sorted data set. It tells us that half of the joggers ran less than 6.05 miles, and half ran more than 6.05 miles.
Mode - Since there is no value that appears more than once in the given data set, there is no mode. The lack of a mode suggests that there is no particular mileage that was most frequently reported.
These statistics provide different measures of central location and give insights into the distribution of the mileage ran by the joggers.