Final answer:
The interquartile range (IQR) for the MPG ratings for cars owned by 15 Placid High School seniors is 11 MPG, calculated by subtracting the first quartile (13 MPG) from the third quartile (24 MPG).
Step-by-step explanation:
Calculating the Interquartile Range (IQR)
The interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles. Quartiles divide a rank-ordered data set into four equal parts. The values that separate parts are called the first quartile (Q1), the median or second quartile (Q2), and the third quartile (Q3). To find the IQR, we subtract Q1 from Q3.
The given data set for the MPG ratings of cars owned by Placid High School seniors is already ordered from lowest to highest:
11, 12, 12, 13, 15, 15, 16, 16, 16, 17, 17, 19, 24, 25, 26
To calculate Q1 (the 25th percentile), find the median of the first half of the data. With 15 data points, the median is the 8th value, so we take the first seven values: 11, 12, 12, 13, 15, 15, 16.
Median (Q1) = 13 (since it's at the middle of the first seven numbers)
For Q3 (the 75th percentile), find the median of the second half of the data. Exclude the overall median and take the last seven values: 16, 17, 17, 19, 24, 25, 26.
Median (Q3) = 24 (since it's at the middle of the last seven numbers)
Finally, calculate the IQR by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 24 - 13 = 11 MPG