The middle 50 percent of the wires of Company A tested between (_______) and (upper) limits. Record ONLY the lower limit as a whole number.

Question

The following statistics represent samples of copper wire submitted by two companies for tensile strength testing (psi).

Statistic                                                      Company A          Company B

Arithmetic Mean                                       500                         600

Median                                                       500                         500

Mode                                                          500                        300

Standard Deviation                                     40                            20

Mean Absolute Deviation                          32                           16

Quartile Deviation                                       25                          14

Range                                                         240                         120

Sample Size                                            100                            80

Answer 1

To get the lower limit, we need to calculate the quartiles of Company A's wire tensile strength distribution.

The quartile deviation of Company A is given as 25, which means that the distance between the first quartile (Q1) and the third quartile (Q3) is 50.

We also know that the median (Q2) is 500.

So, we can write:

Q1 - 500 = -25

Q3 - 500 = 25

Solving for Q1 and Q3, we get:

Q1 = 475

Q3 = 525

The middle 50 percent of the wires fall between Q1 and Q3, so the lower limit is 475, rounded to a whole number. Therefore, the middle 50 percent of the wires of Company A tested between 475 and 525.