Last updated: July 18, 2019
Topic: SocietyWork
Sample donated:

How long it takes to drive to work each day.

Day Time Probabilities
Monday – 30 minutes 0.0968
Tuesday – 35 minutes 0.1129
Wednesday – 30 minutes 0.0968
Thursday – 25 minutes 0.0806
Friday – 35 minutes 0.1129
Monday – 35 minutes 0.1129
Tuesday – 25 minutes 0.0806
Wednesday – 30 minutes 0.0968
Thursday – 30 minutes 0.0968
Friday – 35 minutes 0.1129
TOTAL 310 1

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Day Time Joint Probabilities
Monday – 30 + 35 = 0.2097
Tuesday – 35 + 25 = 0.1935
Wednesday – 30 + 30 = 0.1935
Thursday – 25 + 30 = 0.1774
Friday – 35 + 35 = 0.2258
TOTAL 310 1

I find that the driving times on each day are independent of each other.

1. Calculate the mean, median, and mode.

Mean = (the sum of all its values) / (the number of values).

Monday’s mean = 30 + 35 /2 = 65/2 = 32.5 or 32 ½ or 0.10485

Tuesday’s mean = 35 + 25 /2 = 60/2 = 30 or 0.09675

Wednesday’s mean = 30 + 30 = 60/2 = 30 or 0.09675

Thursday’s mean = 25 + 30 /2 = 55/2 = 27.5 or 27 ½ or 0.0887

Friday’s mean = 35 + 35 = 70 /2 = 35 or 0.1129

Median = 50th percentile of the distribution

Monday’s medium = 30 + 35 /2 = 32.5 or 32 ½ or 0.10485

Tuesday’s medium = 35 + 25 = 60/2 = 30 or 0.09675

Wednesday’s medium = 30 + 30 = 60/2 = 30 or 0.09675

Thursday’s medium = 25 + 30 /2 = 55/2 = 27.5 or 27 ½ or 0.0887

Friday’s medium = 35 + 35 = 70/2 = 35 or 0.1129

Mode = most frequently occurring value/element that occurs most often

Monday’s mode – A data set has no mode when all the numbers appear in the data with the same frequency

Tuesday’s mode – A data set has no mode when all the numbers appear in the data with the same frequency

Wednesday’s mode – A data set has no mode when all the numbers appear in the data with the same frequency

Thursday’s mode – A data set has no mode when all the numbers appear in the data with the same frequency

Friday’s mode – A data set has no mode when all the numbers appear in the data with the same frequency
2. Are these numbers higher or lower than you would have expected?  Just a little lower

3. Which of these measures of central tendency do you think most accurately describes the lifestyle variable you are looking at?  The Mean and the Median (the same)

4. Write a brief paper with your calculations and the answers to these questions.

The mean is the sum of all values divided by the number of values present. In this case, there are two values present so I added the two numbers together and divided that total result by the number of values, which was two values. This gave me my result.

The median is the middle value of the list of numbers. Technically, a list can have more than one mode. The middle value or 50th percentile of the distribution of numbers when operating with two numbers would be the total of the numbers when added together and divided by two. This is how I derived at my calculations for the median set, in this case with a representative of two numbers.

The mode is represented as the most common or most frequent value in a set of numbers. A list can have more than one mode when two or more values appear with the same frequency. However, on the other side of the calculation, a data set would have no modes when all the numbers in the data set appear with the same amount of frequency. This is the case in the data set above.

In general, I felt the values of the mean and median to be slightly lower than what I would have guessed, but not really by much. With the second question regarding the central tendency I think most accurately describes the lifestyle variable I would be looking at, because I have 2 numbers this creates a result in which my mean and median are identical results. Therefore, other than the non-existent mode result, I chose both my mean and my median result.

Overall, I don’t feel there were any great surprises one way or another as far as values that were surprisingly low or surprisingly high. In my representative results I would have to say they were pretty much what I would have expected as my results for the means, medians and modes of the number distributions I was working with.