Frequency Table and Histogram + 2.3: One-Number Summaries

Range - Difference between the largest and the smallest data

When we are presented with a lot of numbers of data, we want to put them in 6 or 7 bins that categorizes them.

Ex. 1-9, 10-19, 20-29, etc…

For frequency tables, tally up how many numbers fit in that bin, total them to a frequency, then make a relative frequency value.

Frequency/Relative Frequency Table Ex. -

Stem-and-Leaf

40 40 35 48 38 40 36 50 32 36 40 35

30 24 40 36 40 36 40 39 33 40 32 38

2 l 4

3 l 5 8

4 l 0 0 8 0 0 0 0 0

5 l 0

Dot Plot

9 9 4 11 10 5 13 9 7 11 6 8 14 10 6

10 10 7 14 11 7 8 6 13 10 14 14 8 13

2.3: One-Number Summaries

Outlier - Data point/entry that is far away from all other data points, sticking out

Mean/Average - Sum of the data divided by the number of data

Population Mean Formula: $\mu=\frac{\sum x}{N}$

Sample Mean Formula: $\overline{x}=\frac{\sum x}{n}$

Example

240 212 270 331 354 283 309 120 237

$\frac{240+212+270+331+354+283+309+120+237}{9}=261.78$ MEAN

Weighted Mean - Mean of a data set whose entries have varying weights

Weighted Mean Formula: $\overline{x}=\frac{\sum xw}{\sum w}$

Example

$\frac{100\cdot0.2+89\cdot0.3+100\cdot0.1+92\cdot0.4}{9}=93.5$ WEIGHTED MEAN

Median - Data set that is the value in the middle of the data when the data is ordered.

Example

120 212 237 240 270 283 309 331 354

270 is the middle, so it is the Median

Mode - The data value that is shown the most frequently.