Math10

• Mean


  The sum of all items or terms divided by the total number of items or terms
• Weighted mean


  The sum of the products formed by multiplying each number by its assigned weight, divided by the sum of all weights
• Median


  The midpoint of the data array, after arranging the data in order from least to greatest or vice versa
• Mode


  The value that occurs most often in the data set
• The data set with one mode is called unimodal, and the data set with two modes is called bimodal
• Group data


  Data which are arranged into a frequency distribution
• Mean of group data

  Σ(fx) / n, where f is the frequency, x is the class mark, and n is the total frequency
• Median of group data

  lb + (Σf/2 - Σf before) / f * i, where lb is the lower boundary of the median class, Σf is the total frequency, Σf before is the cumulative frequency before the median class, f is the frequency of the median class, and i is the class width
• Mode of group data

  lb + (d1 / (d1 + d2)) * i, where lb is the lower boundary of the modal class, d1 is the difference between the frequency of the modal class and the frequency of the class before it, d2 is the difference between the frequency of the modal class and the frequency of the class after it, and i is the class width
• Republic of the Philippines, Department of Education, SCHOOLS DIVISION OF ILOCOS SUR, TAGUDIN NATIONAL HIGH SCHOOL, Tagudin, Ilocos Sur, Together, We Can Make A Difference.
• Weekly Home Learning Plan, April 8-19, 2024, 4th Quarter - MATHEMATICS 10
• Learning Tasks


  1. Pray for guidance to the Almighty God before you start the lesson.

  2. Read and understand the content of this module.

  3. Read and follow the instructions carefully.

  4. Answer the following Activities and Assessment of this modules:
• MODULE 1 - Activities 1 & 2 on page 5, Assessment of page 6
• MODULES 2 - Activities 1 & 2 on page 8, Assessment on page 8
• MODULES 3 - Activities 1 & 2 on page 10, Assessment on pages 10-11
• Quartile


  The score points which divide a distribution into four equal parts
• Decile


  The nine score values that divide a distribution into ten equal parts
• Percentile


  The score values that divide a distribution into one hundred equal parts
• Finding the middle value in a set

  1. Arrange the data in increasing order

  2. The middle value is the median
• Finding the middle value in different data sets

  • -3, 4, -5, -4, 3, -1, 6
  • 9, 1, 6, 8, 3, 2, 2, 4, 1, 5
  • 20, 25, 35, 30, 25, 20, 40, 20, 15
  • 96, 63, 70, 76, 39, 82, 95, 88
  • 750, 680, 728, 800, 615, 850
• Lower Quartile (Q1)


  The value that is between the middle value and the least value in the data set
• Upper Quartile (Q3)


  The value that is between the middle value and the greatest value in the data set
• Finding the lower and upper quartiles

  • Data: 14, 10, 12, 9, 17, 5, 8, 9, 14, 10, 11

  Lower quartile: 9

  Upper quartile: 14
• Finding the average of the lower and upper quartiles

  • Data: 180, 260, 290, 370, 430

  Lower quartile: 260

  Upper quartile: 370

  Average: 315
• Mendenhall and Sincich Method

  To find quartiles:

  Lower Quartile (L) = Position of Q1 = 1/4 (n + 1)

  Upper Quartile (U) = Position of Q3 = 3/4 (n + 1)
• Applying Mendenhall and Sincich Method


  • Data: {1,3,7,7,16,21,27,30,31} and n = 9

  Q1 = 7

  Q3 = 27
• Finding quartiles using Linear Interpolation


  • Data: 1, 3, 7, 7, 16, 21, 27, 30, 31

  Q1 = 5

  Q3 = 28.5
• Deciles are the nine score values that divide a distribution into ten equal parts.
• Finding the 3rd decile (D3)

  • Data: 18, 21, 20, 17, 15, 29, 27, 22, 28

  Steps:

  1. Arrange data in ascending order: 15, 17, 18, 20, 21, 22, 27, 28, 29

  2. Use formula: Dk = k/10(n+1)th position/score

  D3 = 3/10(9+1) = 3/10(10) = 3rd position/score = 17
• The fifth decile (D5) is the median of the set of data
• Steps to find the decile of ungrouped data

  1. Arrange the data in ascending order

  2. Use the formula Dk = k/10(n+1)th position/score

  3. Interpolate if necessary
• Finding the 3rd decile (D3) of a set of data

  • 15, 17, 18, 20, 21, 22, 27, 28, 29
  • D3 = 3/10(9+1) = 3/10(10) = 3rd position/score = 18
• Finding the 7th decile (D7) of a set of data

  • 15, 17, 18, 20, 21, 22, 27, 28, 29
  • D7 = 7/10(9+1) = 7/10(10) = 7th position/score = 27
• Finding D2 and D8 of a set of data

  • 45, 46, 46, 49, 52, 55, 57, 59, 63, 68, 69, 73
  • D2 = 2/10(12+1) = 2/10(13) = 3.9th position/score, interpolated to 48.7
  • D8 = 8/10(12+1) = 8/10(13) = 7.8th position/score, interpolated to 58.6
• Percentile


  Values that separate a set of data into 100 equal groups
• Steps to find the percentile of ungrouped data


  1. Arrange the values in ascending order

  2. Use the formula Pk = k/100(n+1)th position/score

  3. Interpolate if necessary
• Finding the 20th percentile (P20) of a set of data


  • 20, 23, 24, 25, 25, 27, 28, 28, 29, 30
  • P20 = 20/100(10+1) = 2.2th position/score, interpolated to 23.2
• Finding the 30th percentile (P30) of a set of data

  • 29, 35, 38, 38, 42, 43, 45, 54, 54
  • P30 = 30/100(9+1) = 3rd position/score = 38
• Humility is an important virtue, regardless of one's position