Question

score on last try: 0 of 1 pts. see details for more. at least one scored part is incorrect. jump to first changeable incorrect part. > next question you can retry this question below below are the batting averages for 50 baseball players. 0.183 0.185 0.206 0.207 0.209 0.212 0.214 0.221 0.224 0.225 0.228 0.241 0.243 0.249 0.249 0.253 0.256 0.257 0.265 0.271 0.273 0.273 0.273 0.274 0.277 0.279 0.283 0.284 0.286 0.288 0.29 0.291 0.291 0.292 0.295 0.298 0.299 0.302 0.302 0.303 0.305 0.305 0.311 0.312 0.316 0.316 0.319 0.321 0.325 0.327 find the median, q1, and q3 median = q1 = q3 = enter an integer or decimal number more...

Explanation:

Step1: Arrange data in order

The data is already in ascending - order.

Step2: Calculate the median

Since \(n = 50\) (an even - numbered data set), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=25\) and \(\frac{n}{2}+1 = 26\). The 25th value is \(0.273\) and the 26th value is \(0.274\). So, Median\(=\frac{0.273 + 0.274}{2}=0.2735\).

Step3: Calculate \(Q_1\)

The lower half of the data contains the first 25 values. Since \(n_1=25\) (an odd - numbered data set), \(Q_1\) is the \(\frac{25 + 1}{2}=13\)th value in the lower half. The 13th value in the lower half is \(0.243\).

Step4: Calculate \(Q_3\)

The upper half of the data contains the last 25 values. Since \(n_2 = 25\) (an odd - numbered data set), \(Q_3\) is the \(\frac{25+1}{2}=13\)th value in the upper half. The 13th value in the upper half is \(0.299\).

Answer:

Median = \(0.2735\), \(Q_1=0.243\), \(Q_3 = 0.299\)