Question

The following table show the qualifying speeds of race cars at the Indianapolis 500.

Speed (mph) | Number of Cars |

210 - 215 | 8 |

216 - 221 | 15 |

222 - 227 | 32 |

228 - 233 | 40 |

234 - 239 | 9 |

Calculate the weighted population standard deviation for this distribution. Round your answer to the nearest hundredth's place and do not indicate units of measure.

Answer #1

**Solution:**

Class(1) |
Frequency (f)(2) |
Mid value (x)(3) |
f⋅x(4)=(2)×(3) |
f⋅x2=(f⋅x)×(x)(5)=(4)×(3) |

210-215 | 8 | 212.5 | 1700 | 361250 |

216-221 | 15 | 218.5 | 3277.5 | 716133.75 |

222-227 | 32 | 224.5 | 7184 | 1612808 |

228-233 | 40 | 230.5 | 9220 | 2125210 |

234-239 | 9 | 236.5 | 2128.5 | 503390.25 |

-- | n=104 | -- | f⋅x=23510 | f⋅x2=5318792 |

Population Standard deviation is σ

=(
f x2 ) - ((
f x)2 / n ) n

=5318792-(23510)2104
/104

=5318792-5314616.3462/104

=4175.6538/104

=40.1505

=6.336

Population Standard deviation = 6.34

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