Saul decides to use the IQR to measure the spread of the data. Saul calculates the IQR of the data set to be 27.

Saul asks Jasmine to check his work. Saul copies the data in numerical order from least to greatest for Jasmine.

25, 30, 50, 50, 50, 50, 56, n, 250

What is the value of n that will make the IQR of the data set equal to 27?

78

Step-by-step explanation:

The IQR is quartile 3 - quartile 1. First, we need to find the mean of the dataset, which is 50 - - the fifth number. Then, the median of the dataset on the left of the fifth number is the first quartile, and the median of the dataset on the right is the third. We get Q1 to then be halfway between 30 and 50, or 40, and Q3 to be halfway between 56 and n, so Q3 = (56+n) / 2. Since we need Q3-Q1=27, or (56+n) / 2-40=27, we have (56+n) / 2=67 and 56+n=134, so n = 134-56=78