91Ó°ÊÓ

The sample mean is a fundamental concept in statistics that provides a single value representing the center of a data set. When you have a collection of data points, such as the number of emails sent by grandmas in this scenario, the sample mean helps to summarize this information in a concise manner.
To calculate the sample mean, you add up all the observed values and divide the sum by the total number of observations. In this exercise, there were 14 old females who reported sending different numbers of emails. By summing these values (which total to 43) and dividing by 14, we arrive at a sample mean of approximately 3.07.
The sample mean offers a useful snapshot of the data's central tendency and acts as a representative value. It's particularly handy when comparing the central tendencies of different data sets.

Standard deviation is a key measure that expresses the amount of variation or dispersion in a set of data values. If the data points are close to the mean, the standard deviation is small, indicating that the data are clustered closely. Higher values suggest more spread out data.
For our example of grandmas using email, to find the standard deviation of their responses, we first calculated the variance. We subtracted the sample mean from each observed value, squared each difference, and then averaged these squares by dividing them by the number of observations minus one. The square root of this variance gave us a standard deviation of approximately 3.48.
This result suggests that there's a modest amount of variability in how many emails the grandmas sent—some are close to the mean, while there are some outliers.

A confidence interval provides a range, derived from a data sample, that is expected to encompass the true population mean with a specified level of confidence, typically 90%, 95%, or 99%.
From our sample of grandmas, using the 90% confidence interval, we are estimating that the true mean of the whole population of grandmas (if we could sample them all) sending emails could be as low as 1.44 or as high as 4.70. We use the sample mean, standard error, and a critical value from the t-distribution to calculate this range.
This interval helps to understand the reliability of our sample mean as an estimator of the population mean. While the exact true mean might not precisely equal to our sample mean, it is highly likely to fall within this interval.

Skewness characterizes the asymmetry of a distribution. In our exercise, the distribution of emails sent by grandmas is skewed to the right, meaning there are more instances of lower values and fewer high-value outliers.
Right skewness often occurs when a lower bound (like zero) limits data and a few large values make the mean higher than the median. This skewness might hint that many grandmas send few emails, but a small number engage more frequently.
Although skewness suggests the data deviates from a normal distribution, the confidence interval remains valid. Thanks to the Central Limit Theorem, especially with fairly large samples like 14, the sample mean still provides a reliable estimate of the population mean.