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measures of central tendency: mean, median, mode, range find the mean, …

Question

measures of central tendency: mean, median, mode, range
find the mean, median, mode and range for each set of numbers.

  1. 24, 31, 12, 38, 12, 15

median :
mean :
mode :
range :

  1. 5, 28, 16, 32, 5, 16, 48, 29, 5, 35

median :
mean :
mode :
range :

  1. 53, 13, 34, 41, 26, 61, 34, 13, 69

median :
mean :
mode :
range :

  1. 85, 58, 72, 85, 46, 93

median :
mean :
mode :
range :

  1. 92, 63, 22, 80, 63, 71, 44, 35

median :
mean :
mode :
range :

  1. 39, 82, 74, 96, 64, 52, 74

median :
mean :
mode :
range :

  1. 72, 43, 15, 66, 32, 72, 52, 19, 28, 81

median :
mean :
mode :
range :

  1. 40, 90, 36, 68, 90, 11, 88, 54

median :
mean :
mode :
range :

Explanation:

Step1: Recall the definitions

  • Mean: sum of data - points divided by number of data - points.
  • Median: middle value when data is ordered. For an even - numbered data set, it's the average of the two middle values.
  • Mode: the value that appears most frequently.
  • Range: difference between the largest and the smallest value.

Step2: Solve for set 1 (24, 31, 12, 38, 12, 15)

Mean

Sum of data - points: $24 + 31+12 + 38+12+15=132$.
Number of data - points $n = 6$.
Mean $=\frac{132}{6}=22$.

Median

Order the data: $12,12,15,24,31,38$.
Since $n = 6$ (even), median $=\frac{15 + 24}{2}=19.5$.

Mode

The number 12 appears twice, more frequently than other numbers, so mode = 12.

Range

Largest value is 38, smallest is 12. Range $=38 - 12 = 26$.

Step3: Solve for set 2 (5, 28, 16, 32, 5, 16, 48, 29, 5, 35)

Mean

Sum of data - points: $5+28 + 16+32+5+16+48+29+5+35=229$.
Number of data - points $n = 10$.
Mean $=\frac{229}{10}=22.9$.

Median

Order the data: $5,5,5,16,16,28,29,32,35,48$.
Since $n = 10$ (even), median $=\frac{16 + 28}{2}=22$.

Mode

The number 5 appears three times, more frequently than other numbers, so mode = 5.

Range

Largest value is 48, smallest is 5. Range $=48 - 5 = 43$.

Step4: Solve for set 3 (53, 13, 34, 41, 26, 61, 34, 13, 69)

Mean

Sum of data - points: $53+13+34+41+26+61+34+13+69=344$.
Number of data - points $n = 9$.
Mean $=\frac{344}{9}\approx38.22$.

Median

Order the data: $13,13,26,34,34,41,53,61,69$.
Since $n = 9$ (odd), median = 34.

Mode

Both 13 and 34 appear twice, so modes are 13 and 34.

Range

Largest value is 69, smallest is 13. Range $=69 - 13 = 56$.

Step5: Solve for set 4 (85, 58, 72, 85, 46, 93)

Mean

Sum of data - points: $85+58+72+85+46+93=449$.
Number of data - points $n = 6$.
Mean $=\frac{449}{6}\approx74.83$.

Median

Order the data: $46,58,72,85,85,93$.
Since $n = 6$ (even), median $=\frac{72 + 85}{2}=78.5$.

Mode

The number 85 appears twice, so mode = 85.

Range

Largest value is 93, smallest is 46. Range $=93 - 46 = 47$.

Step6: Solve for set 5 (92, 63, 22, 80, 63, 71, 44, 35)

Mean

Sum of data - points: $92+63+22+80+63+71+44+35=470$.
Number of data - points $n = 8$.
Mean $=\frac{470}{8}=58.75$.

Median

Order the data: $22,35,44,63,63,71,80,92$.
Since $n = 8$ (even), median $=\frac{63 + 63}{2}=63$.

Mode

The number 63 appears twice, so mode = 63.

Range

Largest value is 92, smallest is 22. Range $=92 - 22 = 70$.

Step7: Solve for set 6 (39, 82, 74, 96, 64, 52, 74)

Mean

Sum of data - points: $39+82+74+96+64+52+74=481$.
Number of data - points $n = 7$.
Mean $=\frac{481}{7}\approx68.71$.

Median

Order the data: $39,52,64,74,74,82,96$.
Since $n = 7$ (odd), median = 74.

Mode

The number 74 appears twice, so mode = 74.

Range

Largest value is 96, smallest is 39. Range $=96 - 39 = 57$.

Step8: Solve for set 7 (72, 43, 15, 66, 32, 72, 52, 19, 28, 81)

Mean

Sum of data - points: $72+43+15+66+32+72+52+19+28+81=480$.
Number of data - points $n = 10$.
Mean $=\frac{480}{10}=48$.

Median

Order the data: $15,19,28,32,43,52,66,72,72,81$.
Since $n = 10$ (even), median $=\frac{43 + 52}{2}=47.5$.

Mode

The number 72 appears twice, so mode = 72.

Range

Largest value is 81, smallest is 15. Range $=81 - 15 = 66$.

Step9: Solve for set 8 (40, 90, 36, 68, 90, 11, 88, 54)

Mean

Sum of data - points: $40+90+36+68+90+11+88+54=477$.
Number of data - points $n = 8$.
Mean $=\frac{477}{8}=59.625$.

Median

Order the data: $11,36,40,54,68,88,90,90$.
Since $n = 8$ (even), median $=\frac{54 + 68}{2}=61$.

Mode

The…

Answer:

  1. Mean: 22, Median: 19.5, Mode: 12, Range: 26
  2. Mean: 22.9, Median: 22, Mode: 5, Range: 43
  3. Mean: 38.22, Median: 34, Mode: 13 and 34, Range: 56
  4. Mean: 74.83, Median: 78.5, Mode: 85, Range: 47
  5. Mean: 58.75, Median: 63, Mode: 63, Range: 70
  6. Mean: 68.71, Median: 74, Mode: 74, Range: 57
  7. Mean: 48, Median: 47.5, Mode: 72, Range: 66
  8. Mean: 59.625, Median: 61, Mode: 90, Range: 79