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Calculating Mean & Modal Class for Million-Dollar Bonuses
Chapter 3, Problem 13(choose chapter or problem)
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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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,
\(\bar{X}=\frac{150}{30}=5\)