The following data are the top 50 women’s finish time (in minutes) in the 2013 ING New York City Marathon. 161 163 179 179 180 146 149 176 149 150 177 177 164 179 148 177 177 160 158 177 172 160 176 148 166 167 170 171 150 172 173 173 174 175 175 161 152 155 155 176 177 161 176 178 180 145 178 148 181 149 a. Find the mean, median, IQR, and standard deviation. You can use the calculator to find the values. b. Construct a frequency histogram. Begin with a lower-class limit of 140 minutes and class width of 10 minutes. Describe the shape of the distribution. c. On the basis of the histogram you constructed, is the mean a typical finish time? Is the median a typical finish time? d. What does the standard deviation that you found in part a tell us about the spread of the data? Explain what it means in the context of the top 50 women’s finish times for the NYC marathon.
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.
6. The following data are the top 50 women’s finish time (in minutes) in the 2013 ING New York
City Marathon.
161 163 179 179 180 146 149 176 149 150 177 177
164 179 148 177 177 160 158 177 172 160 176 148
166 167 170 171 150 172 173 173 174 175 175 161
152 155 155 176 177 161 176 178 180 145 178 148
181 149
a. Find the
b. Construct a frequency histogram. Begin with a lower-class limit of 140 minutes and class width of 10
minutes. Describe the shape of the distribution.
c. On the basis of the histogram you constructed, is the mean a typical finish time? Is the median a
typical finish time?
d. What does the standard deviation that you found in part a tell us about the spread of the
data? Explain what it means in the context of the top 50 women’s finish times for the NYC
marathon.
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