Question

The accompanying data represents miles per gallon of random sample of cars with a 3 cylinder , 1.0 liter engine

Compute the z score corresponding to the individual who obtained 36.0 miles per gallon interpret the result
Determine the quartiles
compute and interpret the interquartile range IQR
Determine the lower and upper fences and are there any outliers
MPG data
32.7, 36.0, 38.0, 38.6, 40.1, 42.2
34.6, 36.3, 38.1, 38.9, 40.6, 42.7
34.7, 37.3, 38.2, 39.5, 41.4, 43.7
35.3, 37.8, 38.4, 39.7, 41.6, 49.1

Answer 1

The student's question involves computing the z-score for a specific MPG value, determining quartiles, calculating and interpreting the IQR, and identifying outliers within a dataset of MPG data for cars with a specific engine type.

Step-by-step explanation:

The student is asking about how to compute the z-score for an individual data point in a dataset, how to determine the quartiles, calculate and interpret the interquartile range (IQR), and how to find the lower and upper fences to identify any outliers within the given miles per gallon (MPG) data for cars with a 3 cylinder, 1.0 liter engine.

The z-score is calculated by subtracting the mean from the individual data point and then dividing by the standard deviation. For the quartiles and IQR, the data should be organized in ascending order, and then the quartiles can be found using appropriate methods such as splitting the dataset into halves or using percentile formulas. The IQR is the difference between the third and the first quartile. Outliers can be identified by calculating the lower fence (Q1 - 1.5*IQR) and the upper fence (Q3 + 1.5*IQR) and checking which data points fall outside of these boundaries.