Problem

SMART Car The following data represent the miles per gallon of a random sample of SMART cars with a threecylinder, 1.0-liter engine.

31.5 |
36.0 |
37.8 |
38.4 |
40.1 |
42.3 |

34.3 |
36.3 |
37.9 |
38.8 |
40.6 |
42.7 |

34.5 |
37.4 |
38.0 |
39.3 |
41.4 |
43.5 |

35.5 |
37.5 |
38.3 |
39.5 |
41.5 |
47.5 |

Source: www.fueleconomy.gov |

(a) Compute the z-score corresponding to the individual who obtained 36.3 miles per gallon. Interpret this result.

(b) Determine the quartiles.

(c) Compute and interpret the interquartile range, IQR.

(d) Determine the lower and upper fences. Are there any outliers?

Answer :

Step 1 :

Given, the miles per gallon of a random sample of SMART cars with a three cylinder, 1.0-liter engine.

31.5 | 36.0 | 37.8 | 38.4 | 40.1 | 42.3 |

34.3 | 36.3 | 37.9 | 38.8 | 40.6 | 42.7 |

34.5 | 37.4 | 38.0 | 39.3 | 41.4 | 43.5 |

35.5 | 37.5 | 38.3 | 39.5 | 41.5 | 47.5 |

Mean and =3.41

The Test Statistic is given by

Z = -0.73

b) Quartiles

We have n = 24, so for lower quartile we have to add 6th and 7th value and divide it by 2

=...