Math 10 Quarter 4

• Quartiles


  Score points which divide a distribution into four equal parts
• Twenty-five percent (25%) of the distribution fall below the first quartile, fifty percent (50%) fall below the second quartile, and seventy-five percent (75%) fall below the third quartile
• First quartile (Q1)


  The lower quartile, located between the least value and the median
• Second quartile (Q2)


  The median
• Third quartile (Q3)


  The upper quartile, located between the median and the greatest value
• Solving for quartile positions

  Use the formula: Qk = k(n+1)/4, where n is the size of the data set
• Solving for Q1


  Arrange the scores in ascending order

  2. Locate the position of the score in the distribution using the formula

  3. Interpolate to obtain the first quartile
• Solving for Q3


  Arrange the scores in ascending order

  2. Locate the position of the score in the distribution using the formula

  3. Since the position is between two equal values, no interpolation is required
• Inter-quartile range


  The difference between the third quartile and the first quartile
• The position or location of the quartiles can also be solved using the formula: Qk = k(n+1)/4, where n is the size of the data set
• Deciles are the nine score points which divide a distribution into ten equal parts
• Solving for deciles


  Use the formula: Dk = k(n+1)/10
• Percentiles are the ninety-nine score points which divide a distribution into one hundred equal parts so that each part represents 1/100 of the data set
• Solving for percentiles


  Use the formula: Pk = k(n+1)/100
• When data is summarized in tables or frequency distribution, the formulas for quartiles, deciles and percentiles are used to solve for measures of position
• Computing quartiles for grouped data

  Use the formula: Qk = LB + [(kN/4 - cfb)/fQk]i

  Where:

  LB = lower boundary of the Qk class

  N = total frequency

  cfb = cumulative frequency of the class before the Qk class

  fQk = frequency of the Qk class

  i = size of the class interval
• Computing deciles for grouped data

  Use the formula: Dk = LB + [(kN/10 - cfb)/fDk]i

  Where:

  LB = lower boundary of the Dk class

  N = total frequency

  cfb = cumulative frequency of the class before the Dk class

  fDk = frequency of the Dk class

  i = size of the class interval
• Computing percentiles for grouped data

  Use the formula: Pk = LB + [(kN/100 - cfb)/fPk]i

  Where:

  LB = lower boundary of the Pk class

  N = total frequency

  cfb = cumulative frequency of the class before the Pk class

  fPk = frequency of the Pk class

  i = size of the class interval
• Percentile


  Used to characterize values according to the percentage below them
• Calculating the kth percentile (Pk)


  𝑃𝑘 = 𝐿𝐵 + [

  𝑘𝑁

  100 − 𝑐𝑓𝑏

  𝑓𝑃𝑘

  ]𝑖
• LB


  Lower boundary of the 𝑃𝑘 class
• N


  Total frequency
• 𝑐��𝑏


  Cumulative frequency of the class before the 𝑄𝑘 class
• 𝑓��𝑘


  Frequency of the 𝑃𝑘 class
• ��


  Size of the class interval
• The data is for the number of customers coming in daily for 90 days
• Data interpretation is the ultimate reason why we need to learn how to solve measures of position
• Proper interpretation is required to create relevant conclusions
• Quartiles


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


  The nine score points which divide a distribution into ten equal parts
• Percentiles


  The ninety-nine score points which divide a distribution into one hundred equal parts
• 1. The first quartile of the ages of 250 students is 15 years old. Anthony is 15 years old.


  • Anthony will find more students older than him in school
• 2. Mr. Reyes' salary is in the 7th decile

  • Mr. Reyes should be pleased with his salary if he must compare it with the salary of other employees