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Use the following sample data of IQ scores of 40 randomly selected college students to answer parts A-D. 98 148 108 120 111 118 137 115 132 120 132 120 135 121 122 138 141 144 125 126 111 129 128 128 114 130 115 131 117 131 119 134 121 122 139 140 123 143 125 104 (Σx- 5015 and Σ-633815 ) Construct a frequency table and a frequency histogram on the provided table and graph paper. Use 6 classes. Frequency Table 1A Frequency Histogram Class

Use the following sample data of IQ scores of 40 randomly selected college students to answer parts A-D. 98 148 108 120 111 118 137 115 132 120 132 120 135 121 122 138 141 144 125 126 111 129 128 128 114 130 115 131 117 131 119 134 121 122 139 140 123 143 125 104 (Σx- 5015 and Σ-633815 ) Construct a frequency table and a frequency histogram on the provided table and graph paper. Use 6 classes. Frequency Table 1A Frequency Histogram Class

MATLAB: An Introduction with Applications
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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### Educational Exercise on Descriptive Statistics and the Empirical Rule #### C. Descriptive Statistics Find the sample mean, median, mode, sample variance, range, coefficient of variation, and sample standard deviation to the nearest tenth. - **Mean:** ________________ - **Median:** _______________ - **Mode:** ________________ - **Range:** ________________ - **Variance:** ______________ - **Standard Deviation:** ____________ - **Coefficient of Variation:** ______________ #### D. Applying the Empirical Rule On the following bell curve image, model the Empirical Rule using the 40 IQ scores: - By listing the IQ values (to the nearest tenth) pertaining to 1, 2, and 3 standard deviations from the mean on the horizontal axis - Displaying the percent of IQ scores that lie between 1, 2, and 3 standard deviations from the mean between the listed standard deviations under the curve Following the instructions above, answer the questions D1 to D4. #### Bell Curve Diagram Description The diagram above represents the classic bell curve, which is a graphical representation of a normal distribution. The curve is symmetrical, with the peak (indicating the mean score) at the center. The points on the horizontal axis indicate the values of 1, 2, and 3 standard deviations from the mean. #### Questions Using the results, you listed under the curve, determine: **D1. What percentage of the data falls within one standard deviation of the mean?** __________________ **D2. What percentage of the data falls within two standard deviations of the mean?** _________________ **D3. What percentage of the data falls within three standard deviations of the mean?** ________________ **D4. Compare your results to the Empirical Rule. Does this data follow the Empirical Rule? Why or why not?** ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ### Hint The Empirical Rule states that for a normal distribution: - Approximately 68% of the data falls within one standard deviation of the mean. - Approximately 95% of the data falls within two standard deviations of the mean. - Approximately 99.7% of the data falls within three standard deviations of the mean.
Transcribed Image Text:### Educational Exercise on Descriptive Statistics and the Empirical Rule #### C. Descriptive Statistics Find the sample mean, median, mode, sample variance, range, coefficient of variation, and sample standard deviation to the nearest tenth. - **Mean:** ________________ - **Median:** _______________ - **Mode:** ________________ - **Range:** ________________ - **Variance:** ______________ - **Standard Deviation:** ____________ - **Coefficient of Variation:** ______________ #### D. Applying the Empirical Rule On the following bell curve image, model the Empirical Rule using the 40 IQ scores: - By listing the IQ values (to the nearest tenth) pertaining to 1, 2, and 3 standard deviations from the mean on the horizontal axis - Displaying the percent of IQ scores that lie between 1, 2, and 3 standard deviations from the mean between the listed standard deviations under the curve Following the instructions above, answer the questions D1 to D4. #### Bell Curve Diagram Description The diagram above represents the classic bell curve, which is a graphical representation of a normal distribution. The curve is symmetrical, with the peak (indicating the mean score) at the center. The points on the horizontal axis indicate the values of 1, 2, and 3 standard deviations from the mean. #### Questions Using the results, you listed under the curve, determine: **D1. What percentage of the data falls within one standard deviation of the mean?** __________________ **D2. What percentage of the data falls within two standard deviations of the mean?** _________________ **D3. What percentage of the data falls within three standard deviations of the mean?** ________________ **D4. Compare your results to the Empirical Rule. Does this data follow the Empirical Rule? Why or why not?** ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ### Hint The Empirical Rule states that for a normal distribution: - Approximately 68% of the data falls within one standard deviation of the mean. - Approximately 95% of the data falls within two standard deviations of the mean. - Approximately 99.7% of the data falls within three standard deviations of the mean.
### Educational Resource on Frequency Distribution and Histogram Construction #### Problem Statement Use the following sample data of IQ scores of 40 randomly selected college students to answer parts A – D: 98, 148, 108, 120, 111, 118, 137, 115, 132, 120, 135, 121, 122, 138, 141, 144, 125, 126, 111, 129, 128, 118, 144, 130, 113, 151, 117, 131, 119, 124, 121, 122, 139, 140, 123, 143, 125, 104 (\(\sum X = 5015\) and \(\sum X^2 = 638315\)) ### Instructions A. Construct a frequency table and a frequency histogram on the provided table and graph paper. Use 6 classes. #### Frequency Table 1. Calculate the Class Width (CW): \[ CW = \frac{Range}{\# of classes} \] 2. Fill in the Frequency Table. #### Frequency Histogram 1. Plot the classes on the x-axis. 2. Plot the frequencies on the y-axis. 3. Draw bars for each class to represent the frequency. ### Calculation 1. Determine the Range: \[ Range = \text{maximum value} - \text{minimum value} \] 2. Calculate the Class Width: \[ CW = \frac{Range}{6} \] ### Graphical Explanation: The frequency histogram is a bar graph where the x-axis represents the different IQ score classes, and the y-axis represents the frequency of scores within these classes. Each bar height corresponds to the number of students falling within that class interval. ### To Do: - Draw the histogram based on your calculated values. - Provide the frequency table with accurate counts for each class. ### Question B. Based on the histogram, what is the shape of the distribution of college student IQ scores? --- This activity aids in understanding how to group raw data into classes, calculate frequencies, and visualize data distributions using histograms. By interpreting the histogram shape (e.g., normal, skewed, bimodal), students learn essential skills in descriptive statistics.
Transcribed Image Text:### Educational Resource on Frequency Distribution and Histogram Construction #### Problem Statement Use the following sample data of IQ scores of 40 randomly selected college students to answer parts A – D: 98, 148, 108, 120, 111, 118, 137, 115, 132, 120, 135, 121, 122, 138, 141, 144, 125, 126, 111, 129, 128, 118, 144, 130, 113, 151, 117, 131, 119, 124, 121, 122, 139, 140, 123, 143, 125, 104 (\(\sum X = 5015\) and \(\sum X^2 = 638315\)) ### Instructions A. Construct a frequency table and a frequency histogram on the provided table and graph paper. Use 6 classes. #### Frequency Table 1. Calculate the Class Width (CW): \[ CW = \frac{Range}{\# of classes} \] 2. Fill in the Frequency Table. #### Frequency Histogram 1. Plot the classes on the x-axis. 2. Plot the frequencies on the y-axis. 3. Draw bars for each class to represent the frequency. ### Calculation 1. Determine the Range: \[ Range = \text{maximum value} - \text{minimum value} \] 2. Calculate the Class Width: \[ CW = \frac{Range}{6} \] ### Graphical Explanation: The frequency histogram is a bar graph where the x-axis represents the different IQ score classes, and the y-axis represents the frequency of scores within these classes. Each bar height corresponds to the number of students falling within that class interval. ### To Do: - Draw the histogram based on your calculated values. - Provide the frequency table with accurate counts for each class. ### Question B. Based on the histogram, what is the shape of the distribution of college student IQ scores? --- This activity aids in understanding how to group raw data into classes, calculate frequencies, and visualize data distributions using histograms. By interpreting the histogram shape (e.g., normal, skewed, bimodal), students learn essential skills in descriptive statistics.
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