How long do cowboys live: Cowboys have the reputation of being a“hard living, dr
ID: 3252123 • Letter: H
Question
How long do cowboys live: Cowboys have the reputation of being a“hard living, drinking, gambling group of people who are quick to draw and fire their pistols.” In an attempt to either lend credence to or reject this idea, Connie Brooks collected the ages of 32 cowboys who lived in the southwest US around 1890.
58 52 68 86 72 66 97 89 84
91 91 92 66 68 87 86 73 61
70 75 72 73 85 84 90 57 77
76 84 93 58 47
Calculate the mean median and mode. Explain why, based on your data, you would either reject the reputation or think it is credible.
Explanation / Answer
1. Mean:
The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have
Mean=Sum of terms/Number of terms
For the given data we get mean = 2428/32
Mean = 75.9
2. Median:
The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.
Ordering the data from least to greatest, we get:
47 52 57 58 58 61 66 66 68 68 70 72 72 73 73 75 76 77 84 84 84 85 86 86 87 89 90 91 91 92 93 97
As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:
Median=75+76/2=75.5
3. Mode:
The mode of a set of data is the value in the set that occurs most often.
Ordering the data from least to greatest, we get:
47 52 57 58 58 61 66 66 68 68 70 72 72 73 73 75 76 77 84 84 84 85 86 86 87 89 90 91 91 92 93 97
We see that the mode is 84.
If the mean = median= mode then it is in symmetrical dstribution
The given data is in unsymmetrical disribution because Mean, median and mode are not equal.
Therefore we reject the reputaion.
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