Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample1h 1m
- 10. Hypothesis Testing for Two Samples2h 8m
- 11. Correlation48m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
3. Describing Data Numerically
Median
Problem 2.3.62a
Textbook Question
Extending Concepts
Golf The distances (in yards) for nine holes of a golf course are listed.
336 393 408 522 147 504 177 375 360
a. Find the mean and the median of the data.

1
Step 1: To find the mean, sum up all the distances provided in the data set. Use the formula for the mean: , where is the sum of all distances and is the number of data points.
Step 2: Add up all the distances: 336 + 393 + 408 + 522 + 147 + 504 + 177 + 375 + 360. This gives the total sum of the distances.
Step 3: Divide the total sum obtained in Step 2 by the number of data points (9) to calculate the mean.
Step 4: To find the median, first arrange the distances in ascending order: 147, 177, 336, 360, 375, 393, 408, 504, 522.
Step 5: Since there are 9 data points (an odd number), the median is the middle value in the ordered list. Identify the 5th value in the ordered list to determine the median.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Mean
The mean, or average, is calculated by summing all the values in a dataset and then dividing by the number of values. In this case, to find the mean distance of the golf holes, you would add all the distances together and divide by nine, the total number of holes. The mean provides a measure of central tendency that represents the overall average distance.
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Median
The median is the middle value in a dataset when the values are arranged in ascending order. If there is an even number of observations, the median is the average of the two middle numbers. For the golf hole distances, you would first sort the distances and then identify the middle value, which gives insight into the central tendency without being affected by extreme values.
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Data Set
A data set is a collection of related values that can be analyzed to extract meaningful information. In this context, the distances of the nine golf holes form a data set that can be used to calculate statistical measures like the mean and median. Understanding the structure and characteristics of the data set is crucial for accurate analysis.
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