The owner of a coffee shop recorded the number of customers who came into his café each hour in a day. The results were 14, 10, 12, 9, 17, 5, 8, 9, 14, 10, and 11. Find the lower quartile and upper quartile of the data.
To find the lower quartile (Q1) and upper quartile (Q3) of the data, we first need to arrange the data in ascending order:
5, 8, 9, 9, 10, 10, 11, 12, 14, 14, 17
To find Q1 and Q3, we will use the formula:
Q1 = (n + 1) / 4
Q3 = 3 * (n + 1) / 4
where n is the number of data points, which in this case is 11.
Q1 = (11 + 1) / 4 = 3rd data point
Q1 = 3rd data point = 9
Q3 = 3 * (11 + 1) / 4 = 9th data point
Q3 = 9th data point = 14
Therefore, the lower quartile (Q1) is 9 and the upper quartile (Q3) is 14.