### Solution Found!

# Battery Lifetimes: Mean, Variance & Standard Deviation

**Chapter 3, Problem 25**

(choose chapter or problem)

**QUESTION:**

Eighty randomly selected batteries were tested to determine their lifetimes (in hours). The following frequency distribution was obtained. Find the variance and standard deviation for the data.

Class boundaries |
Frequency |

62.5–73.5 |
5 |

73.5–84.5 |
14 |

84.5–95.5 |
18 |

95.5–106.5 |
25 |

106.5–117.5 |
12 |

117.5–128.5 |
6 |

Can it be concluded that the lifetimes of these brands of batteries are consistent?

### Questions & Answers

**QUESTION:**

Eighty randomly selected batteries were tested to determine their lifetimes (in hours). The following frequency distribution was obtained. Find the variance and standard deviation for the data.

Class boundaries |
Frequency |

62.5–73.5 |
5 |

73.5–84.5 |
14 |

84.5–95.5 |
18 |

95.5–106.5 |
25 |

106.5–117.5 |
12 |

117.5–128.5 |
6 |

Can it be concluded that the lifetimes of these brands of batteries are consistent?

**ANSWER:**

Step 1 of 2

We have the data of lifetimes of batteries.

Class boundaries |
Midpoint \(\left(x_{i}\right)\) |
Frequency |

62.5–73.5 |
68 |
5 |

73.5–84.5 |
79 |
14 |

84.5–95.5 |
90 |
18 |

95.5–106.5 |
101 |
25 |

106.5–117.5 |
112 |
12 |

117.5–128.5 |
123 |
6 |

The claim is to find the variance and standard deviation.

#### Watch The Answer!

##### Battery Lifetimes: Mean, Variance & Standard Deviation

Want To Learn More? To watch the entire video and ALL of the videos in the series:

Discover the nuances of analyzing battery lifetime data through mean, variance, and standard deviation computations. Using class boundaries, midpoints, and frequencies, gain insights into the dispersion of battery lifespans and the average deviation from the mean.