| Class interval | Frequency (f) |
|---|---|
| (1, 3] | 16 |
| (3, 5] | 2 |
| (5, 7] | 4 |
| (7, 9] | 3 |
| (9, 11] | 9 |
| (11, 13] | 6 |
Measures of Central Tendency and Variability: Grouped Data
| Class interval | Frequency (f) |
|---|---|
| (1, 3] | 16 |
| (3, 5] | 2 |
| (5, 7] | 4 |
| (7, 9] | 3 |
| (9, 11] | 9 |
| (11, 13] | 6 |
| Class interval | Frequency (f) | Class midpoint (M) |
|---|---|---|
| (1, 3] | 16 | 2 |
| (3, 5] | 2 | 4 |
| (5, 7] | 4 | 6 |
| (7, 9] | 3 | 8 |
| (9, 11] | 9 | 10 |
| (11, 13] | 6 | 12 |
\[Mean = \frac{\sum fM}{\sum f}\]
In-class demo
Plot the histogram.
\[Median = L_M + [\frac{\frac{(\sum f)}{2}-F}{f_M}]W\]
\(L_M\) - lower limit of the class containing the median
\(\sum f\) - total number of observations
\(F\) - the cumulative frequency up to the lower limit of the class containing the median
\(f_M\) - frequency of the class containing the median
\(W\) - width of the class containing the median
\[Q_1 = L_{q1} + [\frac{\frac{(\sum f)}{4}-F_{q1}}{f_{q1}}]W\]
\(L_{q1}\) - lower limit of the class containing the first quartile
\(\sum f\) - total number of observations
\(F_{q1}\) - the cumulative frequency up to the lower limit of the class containing the first quartile
\(f_M\) - frequency of the class containing the median
\(W\) - width of the class containing the median
Your turn: Write the formula for Q3
\[\sigma^2 = \frac{\sum f(M-\mu)^2}{\sum f}\]
\(M\) - Class midpoint
\[s^2 = \frac{\sum f(M-\bar{x})^2}{\sum f -1}\]
\(M\) - Class midpoint