The ten topgrossing movies of a certain film studio are show

The ten top-grossing movies of a certain film studio are shown, in millions of dollars. Complete a and b below. Using the sorted data, find Q1 and Q3. Then find the interquartile range and interpret it in context. Find Q1 and Q3. Q1 = Q3 = (Type integers or decimals.) Find the interquartile range. IQR = (Type an integer or a decimal.)

Solution

Then data in increasing order is

127 132 144 176 188 211 213 254 264 267

Number of data points =10

Q1 is the (1+(10-1)/4 )^th observation.

1+9/4=1+2.25=3.25 (not an integer). Then, Q1 can be calculated using 3^rd and 4^th observations. Since, 3.25 is closers to 3 than to 4th. So, Q1 should be closer to the 3^rd observation than the 4^th observation.

Q1 is (3^rd observation * 0.75 + 4^th observation * 0.25), i.e., Q1=144*0.75+176*0.25 = 152

Again, Q3= (1+(10-1)*3/4)^th observation. 1+9*3/4=7.75

Q3= (7^th observaion * 0.25 + 8^th observation * 0.75)= 213*0.25+254*0.75=243.75

IQR=Q3-Q1=91.75

Thus, the data between the lower 25% and upper 25% differ by 91.75. That means the middle 50% data arranged in increasing (or even if arranged in decreasing) order numerically are spread over a range of 91.75