3.1

13 Mean: 183.1/6=30.52 Median: 29.4+33.2/2=31.3 No mode

14 Mean: 744.8/8=93.1 Median: 85.9+89.9/2=87.9 No mode

15 Mean: 33030/9=3670 Median: 3830 Mode: 4090

16 Mean: 1862/7=266 Median: 266 Mode: 260

17

  1. Because it’s a right skewed histogram, so the mean is greater than the median

  2. Because the histogram is bell-shaped so the mean should be approximately equal to the median

  3. Because the histogram is left skewed so the mean is less than the median

3.2

5 s²=144/5-1=36 s=√144/5-1=6

6 s²=400/5-1=100 s=√400/5-1=10

7 σ²=80/5=16 σ=√80/5=4

8 σ²=576/9=64 σ=√576/9=8

9 s²=1764/9=196 s=√1764/9=14

10 σ²=150/6=25 σ=√150/6=5

14 Range:282-257=25 s=√495718-(1862)²/7/7-1=√71=8.4

24

  1. 6 seconds

  2. The histogram is bell-shaped so it’s ok to use the Empirical Rule

  3. Because 92 is two standard deviations below the mean and 116 is two standard deviations above the mean, 95% of the eruptions would last between 92 and 116 seconds, according to Empirical Rule

  4. Actual percentage: 41/44=93%

  5. Because 98 is one standard deviation below the mean, according to Empirical Rule and base on the graph, 13.5% + 2.35% + 0.15%=16% of the eruptions will last less than 98 seconds

  6. Actual percentage: 5/44=11%