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# Calculating Mean & Modal Class for Million-Dollar Bonuses

**Chapter 3, Problem 13**

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**QUESTION:**

A random sample of bonuses (in millions of dollars) paid by large companies to their executives is shown. Find the mean and modal class for the data.

Class Boundaries | Frequency |
---|---|

0.5-3.5 | 11 |

3.5-6.5 | 12 |

6.5-9.5 | 4 |

9.5-12.5 | 2 |

12.5-15.5 | 1 |

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##### Calculating Mean & Modal Class for Million-Dollar Bonuses

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Learn how to determine the mean and modal class for bonuses in millions. Understand midpoint calculations and how frequencies impact results. Gain insights into bonus distributions in the financial realm.

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### Questions & Answers

**QUESTION:**

A random sample of bonuses (in millions of dollars) paid by large companies to their executives is shown. Find the mean and modal class for the data.

Class Boundaries | Frequency |
---|---|

0.5-3.5 | 11 |

3.5-6.5 | 12 |

6.5-9.5 | 4 |

9.5-12.5 | 2 |

12.5-15.5 | 1 |

**ANSWER:**

Step 1 of 2

(a)

This formula used to determine the Mean for Grouped Data,

\(\bar{X}=\frac{\sum f \cdot X_{m}}{n}\)

where n represents the total number of values in the sample. \(\sum f . X_{m}\) represents the sum of the product of frequency and the midpoint for each class.

The midpoint is sum of lower class boundary and upper class boundary divided by 2, ie;

\(X_{m}=\frac{0.5+3.5}{2}=2\)

Similarly, the remaining class midpoints are shown in the below table. Also the product of frequency and the midpoint for each class are given in the table below:

Class boundaries |
Frequency, |
Midpoint, X |
\(f . X_{m}\) |

0.5–3.5 |
11 |
2 |
22 |

3.5–6.5 |
12 |
5 |
60 |

6.5–9.5 |
4 |
8 |
32 |

9.5–12.5 |
2 |
11 |
22 |

12.5–15.5 |
1 |
14 |
14 |

From the table calculate the sum of the product of frequency and the midpoint for each class, ie;

\(\sum f \cdot X_{m}=22+60+32+22+14=150\)

Then, the Mean for Grouped Data,

\(\bar{X}=\frac{150}{30}=5\)