Question

1. the back - to - back stem and leaf plot below gives the growth in millimeters of 23 flower bulbs planted by a 9^ (th) grade class. the plant heights were measured after one week of growth and after two weeks of growth.

after one week after two weeks
0 6
1 0 2 6 6 7 7 9
2 1 4 4 5 6 7 8 9 9 9 9
3 0 0 0 0 1 2 3 5 6 8 9
4 1 2 3 5 7
write a five - sentence comparing the two distributions.

1. a group of 78 third - grade students in a midwestern elementary school took a \self - concept\ test that measured how well they felt about themselves. higher scores indicate more positive self - concepts. the table below and histogram on the next page give some summary statistics from minitab for these students z - scores.

descriptive statistics: selfconc
variable n mean stdev minimum q1 median q3 maximum
selfconc 78 56.85 12.35 20.00 50.00 59.00 65.00 84.00
(a) one student in the group had a self - concept score of 62. calculate and interpret this students z - score.

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x - \mu}{\sigma}\), where \(x = 62\), \(\mu=56.85\), and \(\sigma = 12.35\).

$$z=\frac{62 - 56.85}{12.35}=\frac{5.15}{12.35}\approx0.42$$

Step2: Interpret the z - score

A z - score of approximately \(0.42\) means that the student's self - concept score of \(62\) is \(0.42\) standard deviations above the mean self - concept score of the group of \(78\) third - grade students.

Answer:

The z - score is approximately \(0.42\). This indicates that the student's score of \(62\) is \(0.42\) standard deviations above the mean score of \(56.85\) for the group.