Does it ever seem to you that the weather is nice during the work week, but lousy on the weekend? Cerveny and Balling (1998) have confirmed that this is not your imagination—pollution accumulating during the work week most likely spoils the weekend weather for people on the Atlantic coast. Consider the following hypothetical data showing the daily amount of rainfall for 10 weeks during the summer.
Week Average Daily Average Daily
Rainfall on Weekdays (Mon-Fri) Rainfall on Weekends (Sat-Sun)
1 1.2 1.5
2 0.6 2.0
3 0.0 1.8
4 1.6 1.5
5 0.8 2.2
6 2.1 2.4
7 0.2 0.8
8 0.9 1.6
9 1.1 1.2
10 1.4 1.7
a. Calculate the average daily rainfall (the mean)
during the week, and the average daily rainfall for
weekends.
b. Based on the two means, does there appear to be a
pattern in the data?
Daily rainfall mean during the week= 99
Daily rainfall mean during the weekend=167
Yes, amount of rainfall in the weekend is more than in the weekdays
mean during the week- 3.53
mean during the weekend- 8.85
To calculate the average daily rainfall for weekdays and weekends, we need to find the mean of the corresponding rainfall data.
a. Calculate the average daily rainfall (the mean) during the week:
To find the mean, we sum up the daily rainfall on weekdays and divide it by the number of weekdays.
Week | Average Daily Rainfall on Weekdays (Mon-Fri)
---------------------------------------------------
1 | 1.2
2 | 0.6
3 | 0.0
4 | 1.6
5 | 0.8
6 | 2.1
7 | 0.2
8 | 0.9
9 | 1.1
10 | 1.4
Sum = 1.2 + 0.6 + 0.0 + 1.6 + 0.8 + 2.1 + 0.2 + 0.9 + 1.1 + 1.4 = 9.9
Number of weekdays = 10
Mean = Sum / Number of weekdays = 9.9 / 10 = 0.99
So, the average daily rainfall during the week is 0.99 inches.
b. Calculate the average daily rainfall for weekends:
To find the mean, we sum up the daily rainfall on weekends and divide it by the number of weekends.
Week | Average Daily Rainfall on Weekends (Sat-Sun)
---------------------------------------------------
1 | 1.5
2 | 2.0
3 | 1.8
4 | 1.5
5 | 2.2
6 | 2.4
7 | 0.8
8 | 1.6
9 | 1.2
10 | 1.7
Sum = 1.5 + 2.0 + 1.8 + 1.5 + 2.2 + 2.4 + 0.8 + 1.6 + 1.2 + 1.7 = 16.7
Number of weekends = 10
Mean = Sum / Number of weekends = 16.7 / 10 = 1.67
So, the average daily rainfall during the weekends is 1.67 inches.
Now, let's analyze the pattern:
Comparing the mean rainfall on weekdays (0.99 inches) to the mean rainfall on weekends (1.67 inches), we can observe that the average daily rainfall is higher on weekends than weekdays. This suggests a pattern of lousy weather on weekends as compared to nicer weather during the work week. This finding supports the idea that pollution accumulating during the work week may be spoiling the weekend weather for people on the Atlantic coast.