5. Two different 5th grade classes take the same test. In the first class of 50 students the mean was 70. In the second class of 20 students the mean was 90. If the two classes arè combined, estimate the overall mean. Find the actual mean. Round to the nearest 100th. Show work.
5. Two different 5th grade classes take the same test. In the first class of 50 students the mean was 70. In the second class of 20 students the mean was 90. If the two classes arè combined, estimate the overall mean. Find the actual mean. Round to the nearest 100th. Show work.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Answer both parts to the question
![**Problem:**
Two different 5th grade classes take the same test. In the first class of 50 students, the mean was 70. In the second class of 20 students, the mean was 90. If the two classes are combined, estimate the overall mean.
___
Find the actual mean. Round to the nearest 100th. Show work.
___
**Solution:**
To find the overall mean when two groups are combined, use the weighted mean formula:
\[
\text{Overall Mean} = \frac{(n_1 \times \text{Mean}_1) + (n_2 \times \text{Mean}_2)}{n_1 + n_2}
\]
Where:
- \( n_1 \) is the number of students in the first class.
- \( \text{Mean}_1 \) is the mean of the first class.
- \( n_2 \) is the number of students in the second class.
- \( \text{Mean}_2 \) is the mean of the second class.
Plug in the values:
- \( n_1 = 50 \)
- \( \text{Mean}_1 = 70 \)
- \( n_2 = 20 \)
- \( \text{Mean}_2 = 90 \)
\[
\text{Overall Mean} = \frac{(50 \times 70) + (20 \times 90)}{50 + 20}
\]
Calculate:
\( 50 \times 70 = 3500 \)
\( 20 \times 90 = 1800 \)
Total sum = \( 3500 + 1800 = 5300 \)
Total number of students = \( 50 + 20 = 70 \)
\[
\text{Overall Mean} = \frac{5300}{70} \approx 75.71
\]
Thus, the overall mean, rounded to the nearest hundredth, is 75.71.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95ac695f-8505-41f1-9a50-01d78715406e%2F73521a41-1dcc-4e5c-ad3e-8fbc8c1f8a59%2F02nhke6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
Two different 5th grade classes take the same test. In the first class of 50 students, the mean was 70. In the second class of 20 students, the mean was 90. If the two classes are combined, estimate the overall mean.
___
Find the actual mean. Round to the nearest 100th. Show work.
___
**Solution:**
To find the overall mean when two groups are combined, use the weighted mean formula:
\[
\text{Overall Mean} = \frac{(n_1 \times \text{Mean}_1) + (n_2 \times \text{Mean}_2)}{n_1 + n_2}
\]
Where:
- \( n_1 \) is the number of students in the first class.
- \( \text{Mean}_1 \) is the mean of the first class.
- \( n_2 \) is the number of students in the second class.
- \( \text{Mean}_2 \) is the mean of the second class.
Plug in the values:
- \( n_1 = 50 \)
- \( \text{Mean}_1 = 70 \)
- \( n_2 = 20 \)
- \( \text{Mean}_2 = 90 \)
\[
\text{Overall Mean} = \frac{(50 \times 70) + (20 \times 90)}{50 + 20}
\]
Calculate:
\( 50 \times 70 = 3500 \)
\( 20 \times 90 = 1800 \)
Total sum = \( 3500 + 1800 = 5300 \)
Total number of students = \( 50 + 20 = 70 \)
\[
\text{Overall Mean} = \frac{5300}{70} \approx 75.71
\]
Thus, the overall mean, rounded to the nearest hundredth, is 75.71.
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