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Approximate the sample mean for the following frequency distribution. Data Frequency 35-38 1 39-42 3 43-46 4 47-50 14 51-54 8 Sample mean- Report answer accurate to one decimal place. Submit Question

Approximate the sample mean for the following frequency distribution. Data Frequency 35-38 1 39-42 3 43-46 4 47-50 14 51-54 8 Sample mean- Report answer accurate to one decimal place. Submit Question

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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### Approximating the Sample Mean for a Frequency Distribution To find the sample mean from a given frequency distribution, follow these steps: 1. **Calculate the midpoint for each data interval** (also known as the class mark). 2. **Multiply each midpoint by the corresponding frequency** to obtain the products. 3. **Sum up all the products** obtained in step 2. 4. **Sum up all the frequencies**. 5. **Divide the sum of the products** by the sum of the frequencies. Here is the given frequency distribution: | Data | Frequency | |--------|-----------| | 35 - 38| 1 | | 39 - 42| 3 | | 43 - 46| 4 | | 47 - 50| 14 | | 51 - 54| 8 | **Steps to Calculate:** 1. **Find Midpoints:** - For 35 - 38: Midpoint = (35+38)/2 = 36.5 - For 39 - 42: Midpoint = (39+42)/2 = 40.5 - For 43 - 46: Midpoint = (43+46)/2 = 44.5 - For 47 - 50: Midpoint = (47+50)/2 = 48.5 - For 51 - 54: Midpoint = (51+54)/2 = 52.5 2. **Multiply Midpoints by Frequencies:** - 36.5 * 1 = 36.5 - 40.5 * 3 = 121.5 - 44.5 * 4 = 178 - 48.5 * 14 = 679 - 52.5 * 8 = 420 3. **Sum of the Products:** - 36.5 + 121.5 + 178 + 679 + 420 = 1435 4. **Sum of the Frequencies:** - 1 + 3 + 4 + 14 + 8 = 30 5. **Calculate Sample Mean:** - Sample Mean = Sum of the Products / Sum of the Frequencies = 1435 / 30 ≈ 47.8 ### Sample Mean Calculation **Sample mean
Transcribed Image Text:### Approximating the Sample Mean for a Frequency Distribution To find the sample mean from a given frequency distribution, follow these steps: 1. **Calculate the midpoint for each data interval** (also known as the class mark). 2. **Multiply each midpoint by the corresponding frequency** to obtain the products. 3. **Sum up all the products** obtained in step 2. 4. **Sum up all the frequencies**. 5. **Divide the sum of the products** by the sum of the frequencies. Here is the given frequency distribution: | Data | Frequency | |--------|-----------| | 35 - 38| 1 | | 39 - 42| 3 | | 43 - 46| 4 | | 47 - 50| 14 | | 51 - 54| 8 | **Steps to Calculate:** 1. **Find Midpoints:** - For 35 - 38: Midpoint = (35+38)/2 = 36.5 - For 39 - 42: Midpoint = (39+42)/2 = 40.5 - For 43 - 46: Midpoint = (43+46)/2 = 44.5 - For 47 - 50: Midpoint = (47+50)/2 = 48.5 - For 51 - 54: Midpoint = (51+54)/2 = 52.5 2. **Multiply Midpoints by Frequencies:** - 36.5 * 1 = 36.5 - 40.5 * 3 = 121.5 - 44.5 * 4 = 178 - 48.5 * 14 = 679 - 52.5 * 8 = 420 3. **Sum of the Products:** - 36.5 + 121.5 + 178 + 679 + 420 = 1435 4. **Sum of the Frequencies:** - 1 + 3 + 4 + 14 + 8 = 30 5. **Calculate Sample Mean:** - Sample Mean = Sum of the Products / Sum of the Frequencies = 1435 / 30 ≈ 47.8 ### Sample Mean Calculation **Sample mean
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