Stem = the first decimal Leaf = the second decimal The display is slightly positively skewed, with two peaks at 4L and 6H, and a gap at 7L.
16. 800 700 600 y 500 c n e u 400 q e r F 300
200 100 0 1
2
3
4
5
6
7
8
9
10
11 11
12
13
14
15
16
Number of Paper Published
a. The graph is highly positively skewed, unimodal, with the peak at t he first class. b. Proportion of authors publishing at least five papers = relative frequency for x = 1 + … +relative frequency for x = 5 = (784+204+127+50+33)/1309 = 1198/1309 = 0.9152 = 91.52% Proportion of authors publishing at least ten papers = relative frequency for x = 1 + … +relative frequency for x = 10 = (784+204+127+50+33+28+19+19+6+7)/1309 (784+204+127+50+33+28+19+19+6+7)/1309 = 1277/1309 = 0.9756 = 97.56% Proportion of authors publishing more than ten papers = 1 - Proportion of authors publishing at least ten papers = 1 – 97.56% = 2.44% c. No. The class has no upper limit. d. Yes. I can create a class 15-17 with three times class width of the other classes. 39. a.
…
…
̄
y~
odd) 1. ( )th ordered value (assuming i is odd)1. orde red value in the old sample sam ple + c = x~ +c ( )th ordered
17
Yimeng Wang
b.
…
2
…
̄
y~
x
()th ordered value (assuming i is odd)1. ()th ordered value in the old sample multiplied by c = c x~
~ x~ y
~
th
th
62. n = 26, Mean = 10.07 Median = average of the 13 and 14 value = 10.6 st rd 1 quartile = 8.9, 3 quartile = 11.2, fourth spread = 11.2 – 8.9 = 2.3, 1.5*fourth spread = 3.45, no outlier, range = 13.1 -6.3=6.8 2 2 2 2 s =sxx= ) /n = 2637.99 – 261.7 /26 = 2637.99 – 2634.11 = 2.88 – ( s = 1.697
∑ ∑
68. a. 25
24.3
) s r 20 e t i L ( n o i t 15 p m u s n 10 o C n e g y 5 x O
23.6
20.85 19.0
18.1
16.65 14.4 11.3 9.6
2.6
0 Weight
Treadmill
No outlier. Treadmill box is more stretched out compared t o the weight box. Treadmill box is more positively skewed and the weight box is slightly more negatively skewed. Treadmill box has a much larger range, and while the max values are the same, the minimum value of treadmill is a lot smaller than that of the weight. The median of the treadmill box is much smaller than that of the weight, not much more than half of the median of the weight. Both whiskers of the treadmill extend longer than those of the weight. 0.4 b. ) s r e -1 t i L ( n -3 o i t p m -5 u s n o C -7 n e g y -9 x O n i e -11 c n e r -13 e f f i D
-15
Difference -2.9
It can be seen in the differences of the two values that, after-treadmill oxygen consumption is consistently larger than that of the after-weight, with a mean difference of -7.2 liters.
-7.2
Whiskers of the plot is more
-9.1
stretched out on the negative side, while the box is more positively skewed, indicating more people with slighter than average
-14.4
difference and some people with very large difference that is twice the value of the median value.
