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Find the mean, median, mode(s), and range of the following data:
1) 5, 3, 2, 5, 2, 5
2) 24, 12, 10, 15, 10, 22, 12
3) 14, 9, 10, 5, 17, 13
4) 21, 15, 16, 25, 25, 13, 18
5) 20, 17, 10, 31, 25, 18, 12
6) 48, 40, 52, 43, 52, 46
7) 9, 15, 28, 10, 8
8) 32, 33, 22, 85, 58
9) 24, 35, 18, 20, 17, 30
10) 116, 130, 120, 125, 140, 125.

Mr. Winters times the speed runners at the school track meet every Friday. This week he ran from one school building to the next. The times in seconds were: 52.6; 61.3; 74.8; 78.2; 86.2; 48.7; 98.2; 78.2; 49.8; 73.5.
Order: 48.7; 49.8; 52.6; 61.3; 73.5; 74.8; 78.2; 78.2; 86.2; 98.2.

11. What is the mean time?
12. What was the most frequent time (mode)?
13. What was the range of the times?

Answer :

To solve this problem, we'll calculate the mean, median, mode(s), and range for each set of data provided.

  1. Data: 5, 3, 2, 5, 2, 5

    • Mean: [tex]\frac{5 + 3 + 2 + 5 + 2 + 5}{6} = \frac{22}{6} \approx 3.67[/tex]
    • Median: Organize the data: 2, 2, 3, 5, 5, 5. The median (middle number) is 3 and 5, so [tex]\frac{3 + 5}{2} = 4[/tex].
    • Mode: The most frequent number is 5 (it appears 3 times).
    • Range: The difference between the largest and smallest number, [tex]5 - 2 = 3[/tex].

  2. Data: 24, 12, 10, 15, 10, 22, 12

    • Mean: [tex]\frac{24 + 12 + 10 + 15 + 10 + 22 + 12}{7} = \frac{105}{7} = 15[/tex]
    • Median: Organize the data: 10, 10, 12, 12, 15, 22, 24. The median is 12.
    • Mode: Both 10 and 12 appear twice, so the modes are 10 and 12.
    • Range: [tex]24 - 10 = 14[/tex].

  3. Data: 14, 9, 10, 5, 17, 13

    • Mean: [tex]\frac{14 + 9 + 10 + 5 + 17 + 13}{6} = \frac{68}{6} \approx 11.33[/tex]
    • Median: Organize the data: 5, 9, 10, 13, 14, 17. The median is [tex]\frac{10 + 13}{2} = 11.5[/tex].
    • Mode: There is no mode since all numbers appear once.
    • Range: [tex]17 - 5 = 12[/tex].

  4. Data: 21, 15, 16, 25, 25, 13, 18

    • Mean: [tex]\frac{21 + 15 + 16 + 25 + 25 + 13 + 18}{7} = \frac{133}{7} \approx 19[/tex]
    • Median: Organize the data: 13, 15, 16, 18, 21, 25, 25. The median is 18.
    • Mode: The mode is 25 (it appears twice).
    • Range: [tex]25 - 13 = 12[/tex].

  5. Data: 20, 17, 10, 31, 25, 18, 12

    • Mean: [tex]\frac{20 + 17 + 10 + 31 + 25 + 18 + 12}{7} = \frac{133}{7} \approx 19[/tex]
    • Median: Organize the data: 10, 12, 17, 18, 20, 25, 31. The median is 18.
    • Mode: There is no mode since all numbers appear once.
    • Range: [tex]31 - 10 = 21[/tex].

  6. Data: 48, 40, 52, 43, 52, 46

    • Mean: [tex]\frac{48 + 40 + 52 + 43 + 52 + 46}{6} = \frac{281}{6} \approx 46.83[/tex]
    • Median: Organize the data: 40, 43, 46, 48, 52, 52. The median is [tex]\frac{46 + 48}{2} = 47[/tex].
    • Mode: The mode is 52 (it appears twice).
    • Range: [tex]52 - 40 = 12[/tex].

  7. Data: 9, 15, 28, 10, 8

    • Mean: [tex]\frac{9 + 15 + 28 + 10 + 8}{5} = \frac{70}{5} = 14[/tex]
    • Median: Organize the data: 8, 9, 10, 15, 28. The median is 10.
    • Mode: There is no mode since all numbers appear once.
    • Range: [tex]28 - 8 = 20[/tex].

  8. Data: 32, 33, 22, 85, 58

    • Mean: [tex]\frac{32 + 33 + 22 + 85 + 58}{5} = \frac{230}{5} = 46[/tex]
    • Median: Organize the data: 22, 32, 33, 58, 85. The median is 33.
    • Mode: There is no mode since all numbers appear once.
    • Range: [tex]85 - 22 = 63[/tex].

  9. Data: 24, 35, 18, 20, 17, 30

    • Mean: [tex]\frac{24 + 35 + 18 + 20 + 17 + 30}{6} = \frac{144}{6} = 24[/tex]
    • Median: Organize the data: 17, 18, 20, 24, 30, 35. The median is [tex]\frac{20 + 24}{2} = 22[/tex].
    • Mode: There is no mode since all numbers appear once.
    • Range: [tex]35 - 17 = 18[/tex].

  10. Data: 116, 130, 120, 125, 140, 125

  • Mean: [tex]\frac{116 + 130 + 120 + 125 + 140 + 125}{6} = \frac{756}{6} = 126[/tex]
  • Median: Organize the data: 116, 120, 125, 125, 130, 140. The median is [tex]\frac{125 + 125}{2} = 125[/tex].
  • Mode: The mode is 125 (it appears twice).
  • Range: [tex]140 - 116 = 24[/tex].

For the special dataset (timing at Mr. Winters's track meet):

  1. Mean time: [tex]\frac{52.6 + 61.3 + 74.8 + 78.2 + 86.2 + 48.7 + 98.2 + 78.2 + 49.8 + 73.5}{10} = 70.13[/tex] seconds.

  2. Mode: The most frequent time is 78.2 seconds (it appears twice).

  3. Range: [tex]98.2 - 48.7 = 49.5[/tex] seconds.

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