Question

probability and statistics
gcw 1.4 displaying quantitative data: stemplots
read each set of directions very carefully. all your work must be shown.
1.)
here are the resting heart rates of 25 ninth - grade biology students.
61 78 77 81 48 75 70 77 70 76 80 55 65 60 63 79 62 71 72 74 74 64 60 71 66 68
make a stemplot of these data. do not split stems.
(a) what percent of these ninth - grade biology students have resting heart rates below 70 beats per minute?
round your answer to one decimal place.
(b) describe the shape of the distribution.
2.)
will children jump farther if they have a target in front of them? to find out, a gym teacher conducted an experiment with 29 six - year - old children. the teacher wrote the names of all 29 children on identical slips of paper, put them in a hat, mixed them up, and drew out 15 slips. each of the 15 selected students did a standing long jump from behind a starting line. the remaining 14 students did a similar standing long jump from behind the starting line, but with a target line placed 200 centimeters from the starting line. the distance from the starting line to the back of each students closest foot was measured (in centimeters). here are the data.
no target: 146 190 109 181 155 167 184 171 157 158 128 157 167 162 137
target: 190 163 142 180 185 170 171 136 184 176 179 188 181 152

Explanation:

Step1: Organize data for stemplot

The data set for resting - heart rates of ninth - grade biology students is: 61 78 77 81 48 75 70 77 70 76 80 55 65 60 63 79 62 71 72 74 74 84 80 71 66 68.
We will create a stemplot where the tens digit is the stem and the units digit is the leaf.
Stemplot:
4 | 8
5 | 5
6 | 0 1 2 3 5 6 8
7 | 0 0 1 1 2 4 4 5 6 7 7 8 9
8 | 0 0 1 4

Step2: Calculate percentage of students with heart rate below 70

Count the number of data points below 70. There are 7 data points (48, 55, 60, 61, 62, 63, 65, 66, 68).
The total number of data points is \(n = 26\).
The percentage formula is \(\text{Percentage}=\frac{\text{Number of favorable data points}}{\text{Total number of data points}}\times100\).
So, \(\text{Percentage}=\frac{7}{26}\times100\approx26.9\%\)

Step3: Describe the shape of the distribution

Looking at the stemplot, the distribution appears to be approximately symmetric. The data is fairly evenly spread out on both sides of the center. There is no strong skew to the left or right.

Answer:

(a) 26.9%
(b) Approximately symmetric