Data Analysis & Probability

1. Data Analysis & Probability M7D1.d – Analyze data with respect to measures of variation (range, quartiles, interquartile range).

2. Words to Know • Range: difference between the greatest and least values in a data set • Quartiles: the three numbers that split an ordered data set in four equal groups • First or Lower quartile: the median of the lower half of the data • Second quartile: the median of the data set • Third or Upper quartile: the median of the upper half of the data • Interquartile range: range in the middle half of the data. It is calculated by subtracting the lower quartile from the upper quartile. (Where about 50% of the data occurs)

3. Example The 11 employees at a company have the following ages: 27, 39, 40, 22, 19, 33, 41, 58, 40, 53, 49 • Order the ages from least to greatest. • 19, 22, 27, 33, 39, 40, 40, 41, 49, 53, 58 • Find range. • Oldest is 58. Youngest is 19. • 58 – 19 = 39. • Range is 39 years.

4. Example Continued • Finding Quartiles. • Second quartile – easiest… just find the median. • 11 numbers, the median is the 6th number which is 40. • Therefore, the Second quartile is 40. • First quartile – find the median of the first half. • 19, 22, 27, 33, 39 – the median of this set is 27. • Therefore the First quartile is 27. • Third quartile – find the median of the second half. • 40, 41, 49, 53, 58 – the median of this set is 49. • Therefore the Third quartile is 49. 19, 22, 27, 33, 39, 40, 40, 41, 49, 53, 58 First Second Third quartile quartilequartile

5. Practice One In their first 9 games, the Braves scored 3, 1, 9, 5, 3, 6, 4, 8, 4 runs. What are the range and the interquartile range of runs scored? • Place them in order from least to greatest. • 1, 3, 3, 4, 4, 5, 6, 8, 9 • Find the range. • Greatest minus least. 9 – 1 = 8. • The Range is 8 runs. • Work as a class to find the lower quartile, the upper quartile and the interquartile. • Answers: Lower quartile – 3 Upper quartile – 7 Interquartile range: 7 – 3 = 4