Question

The following data are the yields, in bushels, of hay from a farmer's last 10 years. Find the IQR. 375, 210, 150, 147, 429, 189, 320, 580, 407, 180 A.265 B. 253 C. 227 D. 279

Answer 1

The interquartile range (IQR) of the farmer's hay yields over the last 10 years is 233.5 bushels. This was determined by ordering the data, calculating the first and third quartiles, and then subtracting the first quartile from the third quartile.

Step-by-step explanation:

To find the Interquartile Range (IQR) of the given yields of hay in bushels, we first need to order the data from smallest to largest. Once we have done this, we then identify the first quartile (Q1) and third quartile (Q3) and subtract Q1 from Q3 to find the IQR.

1. Order the data: 147, 150, 180, 189, 210, 320, 375, 407, 429, 580.
2. Since there are 10 data points, Q1 will be the average of the 2.5th and 3rd data points (which is the value halfway between the second and third values in the ordered list), and Q3 will be the average of the 7.5th and 8th data points (which is the value halfway between the seventh and eighth values in the ordered list).
3. Q1 is halfway between 180 and 189, so Q1 is 184.5. Q3 is halfway between 407 and 429, so Q3 is 418.
4. The IQR is Q3 - Q1, which is 418 - 184.5 = 233.5.

So, the IQR of the yields is 233.5 bushels, which is not listed in the options provided (A. 265, B. 253, C. 227, D. 279). There might be a mistake in the options given, or in the calculation of Q1 and Q3, but based on the information provided and the correct method to find IQR, the answer is 233.5.