Question

a company sells classes on its speed-reading technique, which it advertises to customers through a free, online survey. the results of 10 of these tests are included below. use a ti-83, ti-83 plus, or ti-84 calculator to construct a box and whisker plot for the dataset. what is the value of the first quartile?
words per minute
203
227
212
158
158
254
319
277
263
325
provide your answer below:

Explanation:

Step1: Order the dataset

First, we order the given dataset from smallest to largest. The dataset is: 158, 158, 203, 212, 227, 254, 263, 277, 319, 325.

Step2: Find the median (Q2)

Since there are 10 data points (an even number), the median is the average of the 5th and 6th values. The 5th value is 227 and the 6th value is 254. The median \( Q2=\frac{227 + 254}{2}=\frac{481}{2} = 240.5\). But we are interested in the first quartile (Q1), which is the median of the lower half of the data.

Step3: Determine the lower half

The lower half of the data (values below the median) is: 158, 158, 203, 212, 227.

Step4: Find Q1 (median of lower half)

There are 5 data points in the lower half (an odd number), so the median of this lower half is the 3rd value. The 3rd value in 158, 158, 203, 212, 227 is 203.

Answer:

203