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find the mean, median, mode of the following data. 1) 5, 3, 2, 6, 5, 2,…

Question

find the mean, median, mode of the following data. 1) 5, 3, 2, 6, 5, 2, 5 mean: ____ median: __ mode: __ range: __ 2) 24, 12, 10, 15, 10, 22, 12 mean: __ median: __ mode: __ range: __ 3) 14, 9, 20, 5, 17, 13 mean: __ median: $\frac{13 + 14}{2}=13.5$ mode: none range: $20 - 5 = 15$ 4) 21, 15, 16, 25, 13, 18 mean: __ median: __ mode: __ range: __ 5) 20, 17, 10, 31, 25, 18, 12 mean: __ median: __ mode: __ range: __ 6) 48, 40, 53, 43, 52, 46 mean: __ median: __ mode: __ range: __ 7) 9, 15, 28, 10, 8 mean: __ median: __ mode: __ range: __ 8) 32, 33, 22, 85, 58 mean: __ median: __ mode: __ range: __ 9) 24, 35, 18, 20, 17, 30 mean: __ median: __ mode: __ range: ____ 10) 116, 130, 120, 125, 140, 125 mean: 126 median: 125 mode: 125 range: $\frac{24}{140 - 116}$ 116, 120, 125, 125, 130, 140

Explanation:

Step1: Recall the formulas

Mean = $\frac{\sum_{i = 1}^{n}x_{i}}{n}$, median is the middle - value (or average of two middle - values for even $n$) after arranging data in ascending order, mode is the most frequently occurring value, range = max value - min value.

Step2: Solve for the first data set 5, 3, 2, 6, 5, 2, 5

  • Mean:
  • First, find the sum: $5 + 3+2 + 6+5 + 2+5=28$.
  • There are $n = 7$ data - points. So, mean=$\frac{28}{7}=4$.
  • Median:
  • Arrange in ascending order: 2, 2, 3, 5, 5, 5, 6. The middle value is the 4th value, so median = 5.
  • Mode:
  • The number 5 appears 3 times, more frequently than any other number, so mode = 5.
  • Range:
  • Max value = 6, min value = 2. Range=$6 - 2=4$.

Step3: Solve for the second data set 24, 12, 10, 15, 10, 22, 12

  • Mean:
  • Sum = $24+12 + 10+15+10+22+12=105$.
  • $n = 7$, so mean=$\frac{105}{7}=15$.
  • Median:
  • Arrange in ascending order: 10, 10, 12, 12, 15, 22, 24. The middle value is the 4th value, so median = 12.
  • Mode:
  • 10 and 12 both appear 2 times, so modes are 10 and 12.
  • Range:
  • Max value = 24, min value = 10. Range=$24 - 10=14$.

Step4: Solve for the third data set 14, 9, 20, 5, 17, 13

  • Mean:
  • Sum = $14+9+20+5+17+13=78$.
  • $n = 6$, so mean=$\frac{78}{6}=13$.
  • Median:
  • Arrange in ascending order: 5, 9, 13, 14, 17, 20. Median=$\frac{13 + 14}{2}=13.5$.
  • Mode:
  • No number repeats, so mode = None.
  • Range:
  • Max value = 20, min value = 5. Range=$20 - 5=15$.

Step5: Solve for the fourth data set 21, 15, 16, 25, 13, 18

  • Mean:
  • Sum = $21+15+16+25+13+18=108$.
  • $n = 6$, so mean=$\frac{108}{6}=18$.
  • Median:
  • Arrange in ascending order: 13, 15, 16, 18, 21, 25. Median=$\frac{16 + 18}{2}=17$.
  • Mode:
  • No number repeats, so mode = None.
  • Range:
  • Max value = 25, min value = 13. Range=$25 - 13=12$.

Step6: Solve for the fifth data set 20, 17, 10, 31, 25, 18, 12

  • Mean:
  • Sum = $20+17+10+31+25+18+12=133$.
  • $n = 7$, so mean=$\frac{133}{7}=19$.
  • Median:
  • Arrange in ascending order: 10, 12, 17, 18, 20, 25, 31. The middle value is the 4th value, so median = 18.
  • Mode:
  • No number repeats, so mode = None.
  • Range:
  • Max value = 31, min value = 10. Range=$31 - 10=21$.

Step7: Solve for the sixth data set 48, 40, 53, 43, 52, 46

  • Mean:
  • Sum = $48+40+53+43+52+46=282$.
  • $n = 6$, so mean=$\frac{282}{6}=47$.
  • Median:
  • Arrange in ascending order: 40, 43, 46, 48, 52, 53. Median=$\frac{46 + 48}{2}=47$.
  • Mode:
  • No number repeats, so mode = None.
  • Range:
  • Max value = 53, min value = 40. Range=$53 - 40=13$.

Step8: Solve for the seventh data set 9, 15, 28, 10, 8

  • Mean:
  • Sum = $9+15+28+10+8=70$.
  • $n = 5$, so mean=$\frac{70}{5}=14$.
  • Median:
  • Arrange in ascending order: 8, 9, 10, 15, 28. The middle value is the 3rd value, so median = 10.
  • Mode:
  • No number repeats, so mode = None.
  • Range:
  • Max value = 28, min value = 8. Range=$28 - 8=20$.

Step9: Solve for the eighth data set 32, 33, 22, 85, 58

  • Mean:
  • Sum = $32+33+22+85+58=230$.
  • $n = 5$, so mean=$\frac{230}{5}=46$.
  • Median:
  • Arrange in ascending order: 22, 32, 33, 58, 85. The middle value is the 3rd value, so median = 33.
  • Mode:
  • No number repeats, so mode = None.
  • Range:
  • Max value = 85, min value = 22. Range=$85 - 22=63$.

Step10: Solve for the ninth data set 24, 35, 18, 20, 17, 30

  • Mean:
  • Sum = $24+35+18+20+17+30=144$.
  • $n = 6$, so mean=$\frac{144}{6}=24$.
  • Median:
  • Arrange in a…

Answer:

  1. mean: 4, median: 5, mode: 5, range: 4
  2. mean: 15, median: 12, mode: 10 and 12, range: 14
  3. mean: 13, median: 13.5, mode: None, range: 15
  4. mean: 18, median: 17, mode: None, range: 12
  5. mean: 19, median: 18, mode: None, range: 21
  6. mean: 47, median: 47, mode: None, range: 13
  7. mean: 14, median: 10, mode: None, range: 20
  8. mean: 46, median: 33, mode: None, range: 63
  9. mean: 24, median: 22, mode: None, range: 18
  10. mean: 126, median: 125, mode: 125, range: 24