An annual marathon covers a route that has a distance of approximately 26 miles. Winning times for this marathon are all over 2 hours. The following data are the minutes over 2 hours for the winning male runners over two periods of 20 years each. Earlier Period: 15 19 6 13 10 16 7 17 14 16 23 14 13 20 18 23 22 10 16 13 Recent Period: 7 11 8 9 10 7 10 7 8 14 7 9 7 9 9 9 14 8 9 8 (a) Make a stem-and-leaf display for the minutes over 2 hours of the winning times for the earlier period. Use two lines per stem. (Use the tens digit as the stem and the ones digit as the leaf. Enter NONE in any unused answer blanks. For more details, view How to Split a Stem.) Minutes Beyond 2 Hours - EARLIER PERIOD 0 NONE 0 6 7 1 ? 1 ? 2 0 2 3 3 2 NONE (b) Make a stem-and-leaf display for the minutes over 2 hours of the winning times for the recent period. Use two lines per stem. (Use the tens digit as the stem and the ones digit as the leaf. Enter NONE in any unused answer blanks.) Minutes Beyond 2 Hours - RECENT PERIOD 0 ? ? ? 1 ? ? NONE (c) Compare the two distributions. How many times under 15 minutes are in each distribution? Earlier period ____ times Recent period 20 times.
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.
An annual marathon covers a route that has a distance of approximately 26 miles. Winning times for this marathon are all over 2 hours. The following data are the minutes over 2 hours for the winning male runners over two periods of 20 years each.
Earlier Period:
15 19 6 13 10 16 7 17 14 16 23 14 13 20 18 23 22 10 16 13
Recent Period:
7 11 8 9 10 7 10 7 8 14 7 9 7 9 9 9 14 8 9 8
(a) Make a stem-and-leaf display for the minutes over 2 hours of the winning times for the earlier period. Use two lines per stem. (Use the tens digit as the stem and the ones digit as the leaf. Enter NONE in any unused answer blanks. For more details, view How to Split a Stem.)
Minutes Beyond 2 Hours - EARLIER PERIOD
| 0 | NONE |
| 0 | 6 7 |
| 1 | ? |
| 1 | ? |
| 2 | 0 2 3 3 |
| 2 | NONE |
(b) Make a stem-and-leaf display for the minutes over 2 hours of the winning times for the recent period. Use two lines per stem. (Use the tens digit as the stem and the ones digit as the leaf. Enter NONE in any unused answer blanks.)
Minutes Beyond 2 Hours - RECENT PERIOD
| 0 | ? |
| ? | ? |
| 1 | ? |
| ? | NONE |
(c) Compare the two distributions. How many times under 15 minutes are in each distribution?
Earlier period ____ times
Recent period 20 times.
Introduction:
For the stem-and-leaf display with 2 lines per stem, we have taken leaf values 0 to 4, both inclusive, in the first stem line, and the leaf values 5 to 9, both inclusive, in the second stem line.
For example, consider the values 10, 14, and 15; the first stem line for stem value 1 will contain the leaf value 0 to represent the number 10, and also the leaf value 4 to represent the number 4, whereas the second line will contain the leaf value 5 to represent the number 15.
Note that for each stem, the same leaf value needs to be repeated as many times as the number is in the data set.
For example, as 10 is present in the data set twice, the leaf value 0 will be recorded twice corresponding to the stem value 1.
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