Question

here are 9 pumpkins on adrians farm.
what do you think the values of q1 and q3 are? explain your thinking.
use the sketch tool if it helps to show your thinking.
q1:
q3:
explanation:
share with class
pumpkin weights (pounds)

Explanation:

Step1: Order the data

Assume the weights (from left - to - right on the number line) are \(x_1,x_2,\cdots,x_9\). Let's list them out. If we assume the values (by looking at the number line positions) as \(5,7,15,20,22,24,26,28,36\) (the actual values can be read more accurately if there is a key, but for the sake of illustration). First, we order the data: \(5,7,15,20,22,24,26,28,36\)

Step2: Find the median

The formula for the median position of \(n = 9\) data points is \(M=\frac{n + 1}{2}\)th value. So, \(M=\frac{9+1}{2}=5\)th value. The median \(Q_2=22\)

Step3: Find \(Q_1\)

The lower half of the data is \(n_1 = 4\) data points (\(5,7,15,20\)). The formula for the position of \(Q_1\) for \(n_1\) data points is \(\frac{n_1+1}{2}\)th value. \(\frac{4 + 1}{2}=2.5\)th value. \(Q_1=\frac{7 + 15}{2}=11\)

Step4: Find \(Q_3\)

The upper half of the data is \(n_2=4\) data points (\(24,26,28,36\)). The formula for the position of \(Q_3\) for \(n_2\) data points is \(\frac{n_2 + 1}{2}\)th value. \(\frac{4+1}{2}=2.5\)th value. \(Q_3=\frac{26+28}{2}=27\)

First, order the data. Then, find the median (\(Q_2\)). For \(Q_1\), consider the lower half of the data and use the formula for the median of the lower - half (for \(n = 4\) data points in the lower half, we take the average of the 2nd and 3rd values). For \(Q_3\), consider the upper half of the data and use the formula for the median of the upper - half (for \(n = 4\) data points in the upper half, we take the average of the 2nd and 3rd values).

Answer:

Q1: \(11\)
Q3: \(27\)