This is an old revision of the document!
Table of Contents
Measuring Central Tendency
mean
$$ \begin{equation*}
\text{Sum of all elements} = X_1 + X_2 + X_3 + X_4 + X_5 + . . . + X_n
\end{equation*}
$$
$$ \begin{equation*}
X_1 + X_2 + X_3 + X_4 + X_5 + . . . + X_n = \sum\limits_{i=1}^{n} X_i
\end{equation*}
$$
$$ \begin{equation*}
\frac{\sum\limits_{i=1}^{n} X_i}{n}
\end{equation*}
$$
$$ \begin{equation*}
\mu = \frac{\sum\limits_{i=1}^{n} X_i}{n}
\end{equation*}
$$
|age | 19 | 20 | 21 |
|freq | 1 | 3 | 1 |
$$ \begin{equation*}
\begin{split}
\mu = \frac{\sum\limits_{}^{} \text{fx}}{\sum{\text{f}}}
= \frac{1 \text{x} 19 + 3 \text{x} 20 + 1 \text{x} 21}{5}
\end{split}
\end{equation*}
$$
median
{19, 19, 20, 20, 20, 21, 21, 100, 102}
{19, 20, 20, 20, 21, 21, 100, 102}
e.g.,
- Get mean, median for each data set.
- State how each is skewed.
| value | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| freq | 4 | 6 | 4 | 4 | 3 | 2 | 1 | 1 |
| value | 1 | 4 | 6 | 8 | 9 | 10 | 11 | 12 |
| freq | 1 | 1 | 2 | 3 | 4 | 4 | 5 | 5 |
{1, 1, 1, 2, 2, 2, 2, 3, 3, 31, 31, 32, 32, 32, 32, 33, 33, 33}
{1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 31, 31, 32, 32, 32, 32, 33, 33, 33}
{1, 1, 1, 2, 2, 2, 2, 2, 3, 31, 31, 31, 32, 32, 32, 32, 33, 33, 33}
mode
modality
bimodal
trimodal
multimodal
unimodal
It works for both number measured and category measured data.