Video summary

QUARTILES, DECILES AND PERCENTILES OF UNGROUPED DATA USING MENDENHALL AND SINCICH METHOD

Main summary

Key takeaways

Educational

Main ideas / concepts

  • The video explains how to compute quartiles, deciles, and percentiles for ungrouped data using the Mendenhall and Sincich method.
  • Key definitions:
    • Quartiles: split the ordered data into 4 equal parts.
    • Deciles: split the ordered data into 10 equal parts.
    • Percentiles: split the ordered data into 100 equal parts.

For each type (quartile/decile/percentile), the process is essentially:

  1. Sort the data in ascending order.
  2. Use the corresponding index formula to locate the required position:
    • Quartiles: use ( \dfrac{k(n+1)}{4} ) where (k=1,2,3)
    • Deciles: use ( \dfrac{k(n+1)}{10} ) where (k=1,2,\dots,9)
    • Percentiles: use ( \dfrac{k(n+1)}{100} ) where (k=1,2,\dots,99)
  3. If the position is not a whole number:
    • The video indicates rounding decisions, repeatedly noting patterns like:
      • “round up” for non-integer indices in the examples
      • “round down” for other cases (especially when interpreting lower/upper quartiles)
    • It distinguishes:
      • Lower quartile (Q1) vs Upper quartile (Q3), where rounding direction matters.

Method / instructions (Mendenhall & Sincich) — ungrouped data

General procedure

  • Step 1: List the data values and arrange them in ascending order.
  • Step 2: Let (n) be the number of data points.
  • Step 3: Compute the index position for the desired statistic:
    • Quartiles (Q1, Q2, Q3):
      • ( Q_k ) position (= \dfrac{k(n+1)}{4} )
      • where (k=1) gives Q1, (k=2) gives Q2, (k=3) gives Q3
    • Deciles (D1 to D9):
      • ( D_k ) position (= \dfrac{k(n+1)}{10} )
      • where (k=1,2,\dots,9)
    • Percentiles (P1 to P99):
      • ( P_k ) position (= \dfrac{k(n+1)}{100} )
      • where (k=1,2,\dots,99)
  • Step 4: If the computed position is not an integer:
    • Use rounding as described in the examples.
    • In particular:
      • For Q1 (lower quartile), the example effectively uses rounding down.
      • For Q3 (upper quartile), the example uses rounding up (or the next integer position, as shown).
    • The video also demonstrates rounding choices for deciles/percentiles (often matching the nearest integer position shown in the worked examples).

Specific examples covered

Example 1: Quartiles for 13 students (20-item math quiz)

  • Data (given): (8,\ 12,\ 15,\ 2,\ 7,\ 20,\ 25,\ 9,\ 18,\ 16,\ 6,\ 10,) (and the computation uses (n=13))

  • Process described:

    • Sort into ascending order (video indicates this step).
    • Use formulas to get Q1 and Q3 (Q2 corresponds to the middle position).
    • The video shows intermediate indices like 3.5 (for Q1 position) and 10.5 (for Q3 position).

  • Results stated:

    • Lower quartile (Q1) selected at the 4th data item → value 6
    • Upper quartile (Q3) selected near the 11th data item → value 11
    • (Q2 is implied as the middle/50th percentile for (n=13); the extraction focuses on Q1/Q3.)

Example 2: Quartiles for 10 students (math activity)

  • Scores: (4,\ 9,\ 7,\ 14,\ 10,\ 8,\ 12,\ 15,\ 6,\ 11) → (n=10)

  • Computation inputs described:

    • Q1 position: (0.25(n+1)=0.25(11)=2.75) → rounded up → Q1 at the 3rd item

    • Q2 position: (0.50(n+1)=0.5(11)=5.5) → average/rounding leads to a value around 9.5

    • Q3 position: (0.75(n+1)=0.75(11)=8.25) → rounded down → Q3 at the 8th item

  • Results stated:

    • Q1 = 3
    • Q2 = 9.5
    • Q3 = 8 (Note: the subtitle text is described as somewhat inconsistent in ordering/rounding, but these are the outputs stated by the speaker.)

Example 3: Statistics quiz — Deciles and percentiles

  • Scores (10 items): (4,\ 8,\ 9,\ 12,\ 7,\ 15,\ 14,\ 6,\ 10,\ 11)

  • Task:

    • Find the 3rd decile, 8th decile, and 90th percentile

  • Computations shown (index values):

    • 3rd decile: ( \dfrac{3(n+1)}{10}=\dfrac{3(11)}{10}=3.3 )

    • 8th decile: ( \dfrac{8(n+1)}{10}=\dfrac{8(11)}{10}=8.8 )

    • 90th percentile: ( \dfrac{90(n+1)}{100}=\dfrac{90(11)}{100}=9.9 )

  • Results stated:

    • D3 = 13
    • D8 = 12
    • P90 = 14

Example 4: Bottles of strawberry jam sold — Deciles and percentiles

  • Data: (20,\ 18,\ 16,\ 10,\ 12,\ 15,\ 13,\ 9,\ 11,\ 16,\ 15,\ 16,\ 18,\ 20) → (n=14)

  • Task:

    • 3rd decile, 7th decile, 15th percentile, 80th percentile

  • Computations shown (index values):

    • D3 index: ( \dfrac{3(n+1)}{10}=\dfrac{3(15)}{10}=4.5 )

    • D7 index: ( \dfrac{7(n+1)}{10}=\dfrac{7(15)}{10}=10.5 )

    • P15 index: ( \dfrac{15(n+1)}{100}=\dfrac{15(15)}{100}=2.25 )

    • P80 index: ( \dfrac{80(n+1)}{100}=\dfrac{80(15)}{100}=12 ) (exact integer)

  • Results stated:

    • D3 = 13 (interpreted as “30% fall below 13”)
    • D7 = 16 (interpreted as “70% fall below 16”)
    • P15 = 11
    • P80 = 18 (interpreted as “80% fall below 18”)

Speakers / sources featured

  • No specific person is clearly identified in the subtitles.
  • The video mentions a host identity vaguely, but no definitive speaker name is provided.
  • Source described in the subtitles:
    • “QUARTILES, DECILES AND PERCENTILES OF UNGROUPED DATA USING MENDENHALL AND SINCICH METHOD”
    • The method is attributed to Mendenhall and Sincich.

Original video