You belong to two different walking groups. Here is data about each group’s walking in May 2020. Group A Person Minutes Walking in May 2020 YOU 630 B 400 C 500 D 650 E 350 F 700 G 500 H 550 I 800 K 900 Group B Person Minutes Walking in May 2020 YOU 400 X 250 Y 500 Z 450 Q 650 R 600 Answer the following questions based on this data. What was the Group A mean walking time? By what percent did YOU exceed or fall below the group A mean? Express your answer rounded to the nearest hundredth. What was the Group B median walking time?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
You belong to two different walking groups. Here is data about each group’s walking in May 2020.
Group A
|
Person |
Minutes Walking in May 2020 |
|
YOU |
630 |
|
B |
400 |
|
C |
500 |
|
D |
650 |
|
E |
350 |
|
F |
700 |
|
G |
500 |
|
H |
550 |
|
I |
800 |
|
K |
900 |
Group B
|
Person |
Minutes Walking in May 2020 |
|
YOU |
400 |
|
X |
250 |
|
Y |
500 |
|
Z |
450 |
|
Q |
650 |
|
R |
600 |
Answer the following questions based on this data.
- What was the Group A mean walking time?
- By what percent did YOU exceed or fall below the group A mean? Express your answer rounded to the nearest hundredth.
- What was the Group B
median walking time?
- By what percent did YOU exceed or fall below the group B median? Express your answer rounded to the nearest hundredth.
- Let’s suppose you want to draw a pie chart that shows information for the members of each group classified by a rating based on the amount of walking time. There will be 4 categories: excellent, very good, good, needs improvement.
The Needs Improvement category is for the percentage of group members who walked for less than 400 minutes.
Which group [A or B] has the smaller percentage of members in the Needs Improvement category? What is that percentage? Express your answer to the nearest hundredth.
- One other way to look at the data is by percentiles. In which group was YOUR percentile rank higher? What is that percentile? Round the percentiles to the nearest whole number.
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