• Dataset: built-in R dataset airquality.
• Daily maximum temperatures in New York, May–September 1973.
• Goal: estimate the average daily maximum temperature.

The sample mean estimates the average temperature:

\[\hat{\mu}=\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_i\]

Here, \(x_i\) is a daily maximum temperature in °F.

The sample standard deviation describes temperature variation:

\[s=\sqrt{\frac{\sum_{i=1}^{n}(x_i-\bar{x})^2}{n-1}}\]

A larger \(s\) means temperatures vary more between days.

n <- nrow(weather)
average_temp <- mean(weather$Temp)
sd_temp <- sd(weather$Temp)
round(c(Days = n, Mean_F = average_temp, SD_F = sd_temp), 2)

##   Days Mean_F   SD_F 
## 153.00  77.88   9.47

• Estimated mean daily maximum: 77.88 °F.
• Sample standard deviation: 9.47 °F.
• These results describe the observed May–September 1973 temperatures, not a weather forecast.