3.1

13 Mean: (34.0+33.2+37.0+29.4+23.6+25.9)/6 = 30.5 miles/gallon Median: 23.6, 25.9, 29.4, 33.2, 34.0, 37.0 = (29.4+33.2)/2 = 31.3 mpg. Mode: There is no mode.

14 Mean: (60.5+128.0+84.6+122.3+78.9+94.7+85.9+89.9)/8 = 93.1 Median: 60.5, 78.9, 84.6, 85.9, 89.9, 94.7, 122.3, 128.0 = (85.9+89.9)/2 = 87.9 Mode: There is no mode.

15 Mean: (3960+4090+3200+3100+2940+3830+4090+4040+3780)/9 = 3670 Median: 2940, 3100, 3200, 3780, 3830, 3960, 4040, 4090, 4090 = 3830 Mode: 4090

16 Mean: (282+270+260+266+257+260+267)/7 = 266 Median: 257, 260, 260, 266, 267, 270, 282 = 266 Mode: 260

17

  1. In this histogram, the mean is greater than the median. The histogram is skewed to the right so the mean will be bigger than the median.

  2. The mean is approximately equal to the median because the histogram appears to be fairly bell-shaped.

  3. The mean is less than the median because the histogram is skewed to the left.

3.2

5 Sample standard deviation = 6 Sample variance = 36

6 Sample standard deviation = 10 Sample variance = 100

7 Population standard deviation = 4 Population variance = 16

8 Population standard deviation = 8 Population variance = 64

9 Sample standard deviation = 14 Sample variance = 196

10 Population standard deviation = 5 Population variance = 25

14 Range = 282 - 257 = 25 Sample standard deviation = 8.43

24

  1. 6 seconds

  2. We can use the Empirical Rule to determine basic values that fall around the mean, or average, length of eruption. We can determine percentages of values that fall close to the mean, farther away from the mean, etc.

  3. 95% of eruptions last between 92 and 116 seconds.

  4. About 93.2% of eruptions actually last between 92 and 116 seconds.

  5. 16% of eruptions last less than 98 seconds according to the Empirical Rule.

  6. About 11.4% of eruptions actually last less than 98 seconds.