Statistical Analysis of Datasets

Statistical Analysis of Datasets

Dataset 1: 3, 6, 5, 6, 7, 3

  • Step 1: Determine Largest and Smallest Numbers

    • Largest number: 7

    • Smallest number: 3

  • Step 2: Calculate the Range

    • Calculation: 7 - 3 = 4

    • Range: 4

Dataset 2: 16, 28, 13, 25, 28, 28, 30

  • Step 1: Calculate the Mean

    • Sum of the numbers: 16 + 28 + 13 + 25 + 28 + 28 + 30 = 168

    • Number of elements in the dataset: 7

    • Calculation: 168 / 7 = 24

    • Mean: 24

  • Step 2: Determine the Median

    • Arrange numbers in ascending order: 13, 16, 25, 28, 28, 28, 30

    • Center number (4th number in a dataset of 7 elements): 28

    • Median: 28

  • Step 3: Establish the Mode

    • Number frequency: 28 appears 3 times, others appear less frequently

    • Mode: 28

  • Step 4: Calculate the Range

    • Calculation: 30 - 13 = 17

    • Range: 17

Dataset 3: 69, 32, 43, 36, 45, 29, 32, 79, 69, 76

  • Step 1: Calculate the Mean

    • Sum of the numbers: 69 + 32 + 43 + 36 + 45 + 29 + 32 + 79 + 69 + 76 = 510

    • Number of elements in the dataset: 10

    • Calculation: 510 / 10 = 51

    • Mean: 51

  • Step 2: Determine the Median

    • Arrange numbers in ascending order: 29, 32, 32, 36, 43, 45, 69, 69, 76, 79

    • Center numbers (5th and 6th numbers in a dataset of 10 elements): 43 and 45

    • Calculation: (43 + 45) / 2 = 44

    • Median: 44

  • Step 3: Establish the Mode

    • Number frequency: 32 appears twice, 69 also appears twice.

    • Modes: 32 and 69

  • Step 4: Calculate the Range

    • Calculation: 79 - 29 = 50

    • Range: 50

Dataset 4: 7/8, 10/16, 1/2, 1/3, 1/6

  • Step 1: Calculate the Mean

    • Sum of the numbers: ( rac{7}{8} + rac{10}{16} + rac{1}{2} + rac{1}{3} + rac{1}{6} = 2.5 )

    • Number of elements in the dataset: 5

    • Calculation: 2.5 / 5 = 0.5

    • Mean: 1/2

  • Step 2: Determine the Median

    • Convert fractions to a common denominator and arrange in ascending order: ( rac{1}{6}, rac{1}{3}, rac{1}{2}, rac{10}{16}, rac{7}{8} )

    • Center number: 1/2

    • Median: 1/2

  • Step 3: Establish the Mode

    • Each number appears only once

    • Mode: No mode

  • Step 4: Calculate the Range

    • Calculation: ( rac{7}{8} - rac{1}{6} = rac{17}{24} )

    • Range: 17/24