Measures of Variability (Ungrouped Data) . Compute for the range, the mean deviation, the variance and the standard deviation for the set of data. 1.7,12,11,8,13,9 R=13-7 MD= [(7-10) + (12-10) + (11-10) + (8-10) + (13-10) + (9-10)] 3+2+1+2+3+1 V = (7-1077 (12-10) 7 (11-10 3² + (8-10)² + (13-10) + (9-10)² SD = √516 = 2.31 N C 12 66 2. 18,17,24,24,17,25,24,22,24,25 R = 25-17 = 8 MD= [ (18-21.6)+ (17-21.6) + (24-21.6) + (24-21-6)+(17-21.6)+(25-21.6) + (24-216) + (22-2116) +(24-21.6) (25-216)] = 2.64 3. 123,120,111,107,118,100,99 = 2 5. 92,92,89,88,81,91,93,90,95,87 10 4. 18.1,16.3,14.2, 18.0,9.5, 7.6,12.3,11.5,12.4 = 9+4+1+4+9+1 5 = 5.6 28 5 2 V = {(18-21.6) ²7 (17= 21.6) +- (24-21.6) (24-21.657 (17-21. 6) + (25-21.63 + (24-21.63 +(22-21. 63+ (24-21.65 + (25-21.61 9
Measures of Variability (Ungrouped Data) . Compute for the range, the mean deviation, the variance and the standard deviation for the set of data. 1.7,12,11,8,13,9 R=13-7 MD= [(7-10) + (12-10) + (11-10) + (8-10) + (13-10) + (9-10)] 3+2+1+2+3+1 V = (7-1077 (12-10) 7 (11-10 3² + (8-10)² + (13-10) + (9-10)² SD = √516 = 2.31 N C 12 66 2. 18,17,24,24,17,25,24,22,24,25 R = 25-17 = 8 MD= [ (18-21.6)+ (17-21.6) + (24-21.6) + (24-21-6)+(17-21.6)+(25-21.6) + (24-216) + (22-2116) +(24-21.6) (25-216)] = 2.64 3. 123,120,111,107,118,100,99 = 2 5. 92,92,89,88,81,91,93,90,95,87 10 4. 18.1,16.3,14.2, 18.0,9.5, 7.6,12.3,11.5,12.4 = 9+4+1+4+9+1 5 = 5.6 28 5 2 V = {(18-21.6) ²7 (17= 21.6) +- (24-21.6) (24-21.657 (17-21. 6) + (25-21.63 + (24-21.63 +(22-21. 63+ (24-21.65 + (25-21.61 9
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 numbers 3 to 5 only
Transcribed Image Text:# Measures of Variability (Ungrouped Data)
### Instructions:
Compute for the range, the mean deviation, the variance, and the standard deviation for each set of data.
### Example 1:
**Data Set:** 7, 12, 11, 8, 13, 9
1. **Range (R):**
- \( R = 13 - 7 = 6 \)
2. **Mean Deviation (MD):**
- \( MD = \frac{|7-10| + |12-10| + |11-10| + |8-10| + |13-10| + |9-10|}{6} \)
- \( MD = \frac{3 + 2 + 1 + 2 + 3 + 1}{6} \)
- \( MD = \frac{12}{6} = 2 \)
3. **Variance (V):**
- \( V = \frac{(7-10)^2 + (13-10)^2 + (11-10)^2 + (8-10)^2 + (13-10)^2 + (9-10)^2}{6} \)
- \( V = \frac{9+4+1+4+9+1}{6} \)
- \( V = \frac{28}{6} = 4.67 \)
4. **Standard Deviation (SD):**
- \( SD = \sqrt{V} = \sqrt{4.67} \approx 2.16 \)
### Example 2:
**Data Set:** 18, 17, 24, 24, 17, 25, 24, 22, 24, 25
1. **Range (R):**
- \( R = 25 - 17 = 8 \)
2. **Mean Deviation (MD):**
- \( MD = \frac{\sum|X_i - \overline{X}|}{n} \)
- Calculate \( \overline{X} (Mean) = \frac{18 + 17 + 24 + 24 + 17 + 25 + 24 + 22 + 24 + 25}{10} = 22 \)
- \( MD = \frac{(18-22) + (17-22) + (
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