# 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

##### 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.

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

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, f 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,

$$\bar{X}=\frac{150}{30}=5$$