The nicotine contents, in milligrams, for 40 cigarettes of a...

The nicotine contents, in milligrams, for 40 cigarettes of a certain brand were recorded as follows: $$ \begin{array}{rrrrr} 1.09 & 1.92 & 2.31 & 1.79 & 2.28 \\ 1.74 & 1.47 & 1.97 & 0.85 & 1.24 \\ 1.58 & 2.03 & 1.70 & 2.17 & 2.55 \\ 2.11 & 1.86 & 1.90 & 1.68 & 1.51 \\ 1.64 & 0.72 & 1.69 & 1.85 & 1.82 \\ 1.79 & 2.46 & 1.88 & 2.08 & 1.67 \\ 1.37 & 1.93 & 1.40 & 1.64 & 2.09 \\ 1.75 & 1.63 & 2.37 & 1.75 & 1.69 \end{array} $$ (a) Find the sample mean and sample median. (b) Find the sample standard deviation.

The nicotine contents, in milligrams, for 40 cigarettes of a certain brand were recorded as follows:
$$
\begin{array}{rrrrr}
1.09 & 1.92 & 2.31 & 1.79 & 2.28 \\
1.74 & 1.47 & 1.97 & 0.85 & 1.24 \\
1.58 & 2.03 & 1.70 & 2.17 & 2.55 \\
2.11 & 1.86 & 1.90 & 1.68 & 1.51 \\
1.64 & 0.72 & 1.69 & 1.85 & 1.82 \\
1.79 & 2.46 & 1.88 & 2.08 & 1.67 \\
1.37 & 1.93 & 1.40 & 1.64 & 2.09 \\
1.75 & 1.63 & 2.37 & 1.75 & 1.69
\end{array}
$$
(a) Find the sample mean and sample median.
(b) Find the sample standard deviation.

Key Concepts

Sample Standard Deviation

The sample standard deviation is a measure of the amount of variation or dispersion in a set of values. It is computed by first finding the variance, which involves taking the squared differences between each observation and the sample mean, summing these squares, and dividing by the sample size minus one (n-1). The standard deviation is the square root of this variance and gives an indication of how spread out the values are around the mean.

Descriptive Statistics

Descriptive statistics involves summarizing and organizing data using measures of central tendency and measures of variability. It includes statistics like the mean, median, and standard deviation, which provide a snapshot of the data's overall distribution without making inferences about a larger population.

Sample Mean

The sample mean is the arithmetic average of a set of data points. It is calculated by summing all the observed values and then dividing by the number of observations. This measure provides a central value for the dataset and is fundamental in statistical analyses.

Sample Median

The sample median is the middle value in an ordered dataset. When the data is arranged from the smallest to largest, the median separates the dataset into two equal halves. It is particularly useful as a robust measure of central tendency, especially when the data is skewed or contains outliers.

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