Question

next, find q1. recall that the first quartile q1 is the median of the lower half of the data. that is, the median of the data located below the q2 position. consider the ordered list of data values. the location of the median (q2), which was determined in the last step, is indicated for clarity. 11, 14, 16, 17, 17, 20, 21, 23, 29, 32, q2, 32, 34, 35, 36, 37, 38, 40, 45, 45, 51 there are twenty values in the whole data set, but there are only blank values to the left of the median. the first quartile q1 will be equal to the median of these values. since the lower half of the data has an even number of data values, we will now use the rule to find the median of an even number of data values. median = sum of middle two values / 2 the middle two values of the lower half of the data set are 17 and blank. now, calculate the first quartile, q1. q1=(17 + blank)/2

Explanation:

Step1: Determine number of values in lower - half

There are 20 values in total. The number of values to the left of the median (lower - half) is $\frac{20}{2}=10$.

Step2: Identify middle two values in lower - half

The ordered list of lower - half values is 11, 14, 16, 17, 17, 20, 21, 23, 29, 32. The middle two values are 17 and 20.

Step3: Calculate first quartile $Q_1$

Using the formula $Q_1=\frac{17 + 20}{2}=\frac{37}{2}=18.5$.

Answer:

18.5