numerical method in statistics (MEAN AND MEDIAN)
This document provides formulas and examples for calculating the mean and median of data sets. It defines the mean as the sum of all values divided by the total number of data points. For grouped data, the mean is calculated as the sum of the frequency multiplied by the midpoint of each class, divided by the total number of data points. Examples are provided to demonstrate calculating the mean of both ungrouped and grouped data sets. The median is defined for grouped data as the lower boundary of the class containing the median plus the class width times the amount the cumulative frequency is less than the halfway point, divided by the total number of data points. An example is given to demonstrate calculating the median of a grouped data set.
numerical method in statistics (MEAN AND MEDIAN)
- 1. NUMERICAL METHOD REPORTED BY: Angel Grace Adem
- 2. MEAN( 𝑥 ) FORMULA: Ungrouped Data : 𝑥 = 𝑥1+𝑥2+⋯ 𝑥 𝑛 𝑛 Group Data: 𝑥 = 𝑓𝑥 𝑛 where: f = frequency in each class x= midpoint of each class n= total number of scores
- 3. MEAN( 𝑥 ) EXAMPLES (ungrouped Data): 1. Find the mean of 5, 7, 11, 20 and 18. SOLUTION: 𝑥 = 5 + 7 + 11 + 20 + 18 5 = 61 5 = 12.2
- 4. MEAN( 𝑥 ) 2. Find the Weighted Arithmetic mean of the numbers 12, 15, 16,12, 15, 18, 18, 20, 12 and 18. SOLUTION: 𝑥 = 12 3 +15 2 +18 3 +16+20 3+2+3+1+1 = 36+30+54+36 10 = 156 10 = 15.6
- 5. MEAN( 𝑥 ) 3. The class standing of a student is 84, while the preliminary examination is 75. Compute the preliminary grade if the weighted of the class standing is 2 and the preliminary examination is 1.
- 6. MEAN( 𝑥 ) SOLUTION: 𝑥 = 2 3 84 + 1 3 79 = 168 3 + 79 3 = 247 3 = 82.33
- 7. MEAN( 𝑥 ) Example (grouped data): 1. SOLUTION: 𝑥 = 𝑓𝑥 𝑛 𝑥 = 186 33 𝑥 = 5.636 or 5.64 Interv al Midpoint Frequen cy (𝒇𝒙) 1-3 2 7 14 4-6 5 12 60 7-9 8 14 112 n=33 𝑓𝑥 = 186
- 8. MEAN( 𝑥 ) 2. On arriving in the Beach of Boracay, a sample of 60 vacationers is asked about their ages by the Tourist Bureau. The Sample information is organized into the following frequency distribution. Compute the mean age. SOLUTION: 𝑥 = 𝑓𝑥 𝑛 𝑥 = 2540 60 𝑥 =42.33 Age No. of Vacatione r (𝒇) Midpoint (x) (𝒇𝒙) 11-20 5 15.5 77.5 21-30 7 25.5 178.5 31-40 12 35.5 426 41-50 22 45.5 1001 51-60 8 55.5 444 61-70 4 65.5 262 71-80 2 75.5 151 n=60 𝑓𝑥 = 2540
- 9. MEAN( 𝑥 ) 3. Compute the new salary of the 20 employees in the ABC Company organized in the frequency distribution as follows: SOLUTION: 𝑥 = 𝑓𝑥 𝑛 𝑥 = 5910 20 𝑥 =295.5 Salary of Employees 𝒇 x (𝒇𝒙) 101-200 4 150. 5 602 201-300 9 250. 5 2254.5 301-400 3 350. 5 1051.5 401-500 2 450. 5 901 501-600 2 550. 5 1101 n=20 𝑓𝑥 = 5910
- 10. MEDIAN 𝑥 FORMULA Grouped Data : 𝑥 = 𝐿 𝑏 + 𝑛 2 −𝐶𝐹< 𝑓 𝑚 ∙ 𝑐 Where: 𝐿 𝑏 =lower class containing the median 𝐶𝐹< = less than cumulative frequency 𝑓𝑚 = frequency of the class containing median c = width of the class n = number of sample
- 11. MEDIAN 𝑥 FORMULA (ungrouped data): 𝑥 = 𝑛+1 2 Where: n= number of sample
- 12. MEDIAN 𝑥 EXAMPLE 1. Following distribution of Mathematics scores of 20 students: 𝒙 = 𝑳 𝒃 + 𝒏 𝟐 −𝑪𝑭< 𝒇 𝒎 ∙ 𝑐 𝒙 = 4.5 + 𝟐𝟎 𝟐 −𝟒 𝟖 ∙ 𝑐 𝒙 = 4.5 + 10−4 8 ⋅ 2 𝒙 = 6 Scores Number of Students CF 1-2 1 1 3-4 3 4 𝐶𝐹< = 4 5-6 8 12 𝐿 𝑏 = 4.5 7-8 6 18 9-10 2 20