Use the sample mean(78.5)and sample standard deviation (12.3671)in your calculations below. Use appropriate symbols throughout.Would someone with an overall grade average of 87 be considered “extreme” or “typical”? Provide an explanation why with your answer. **Scenario:** Two researchers are examining academic success. They use the same set of 10 high school student participants, but they each measure academic success differently. Researcher 1 measures academic success by asking the participants to self-report which letter grade is most typical for them to receive on an assignment on the standard A through F scale. Researcher 2 measures academic success by accessing the students’ academic records and retrieving their overall grade average from the school’s system. The participants’ scores are shown below.| Researcher 1: Typical Letter Grade | Researcher 2: Overall Grade Average ||-------------------------------------|--------------------------------------|| B | 85 || A | 96 || C | 75 || B | 86 || A | 90 || D | 60 || D | 59 || B | 84 || B | 80 || C | 70 |**Explanation of the Table:**The table presents the academic success of students as measured by two different methods. For Researcher 1, the students self-reported their most typical letter grades, ranging from A to D. For Researcher 2, the overall grade averages, given as numerical scores ranging from 59 to 96, were recorded from school records. This comparison allows for an analysis of the potential differences in self-perception of academic success versus actual academic performance.

Answered: Use the sample mean(78.5)and sample…

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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Question

Use the sample mean(78.5)and sample standard deviation (12.3671)in your calculations below. Use appropriate symbols throughout. Would someone with an overall grade average of 87 be considered “extreme” or “typical”? Provide an explanation why with your answer.

**Scenario:** Two researchers are examining academic success. They use the same set of 10 high school student participants, but they each measure academic success differently. Researcher 1 measures academic success by asking the participants to self-report which letter grade is most typical for them to receive on an assignment on the standard A through F scale. Researcher 2 measures academic success by accessing the students’ academic records and retrieving their overall grade average from the school’s system. The participants’ scores are shown below.

| Researcher 1: Typical Letter Grade | Researcher 2: Overall Grade Average |
|-------------------------------------|--------------------------------------|
| B | 85 |
| A | 96 |
| C | 75 |
| B | 86 |
| A | 90 |
| D | 60 |
| D | 59 |
| B | 84 |
| B | 80 |
| C | 70 |

**Explanation of the Table:**

The table presents the academic success of students as measured by two different methods. For Researcher 1, the students self-reported their most typical letter grades, ranging from A to D. For Researcher 2, the overall grade averages, given as numerical scores ranging from 59 to 96, were recorded from school records. This comparison allows for an analysis of the potential differences in self-perception of academic success versus actual academic performance.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1: Solution

Given that:

$top enclose x equals space 78.5 space s a m p l e space m e a n space s equals 12.3671 space s a m p l e space s tan d a r d space d e v i a t i o n space$