Question

Hi please help me with my stats hw if anyone can be my tutor that would be awesome

Answer 1

Answers:

mean = 67.6 km

median = 56 km

mode = 56 km

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Step-by-step explanation

To get the mean, we add up the values and then divide by the sample size. The sample size is how many numbers there are in the list.

Add: 51+108+40+177+56+64+32+32+72+37+64+48+121+56+56 = 1014

Divide by sample size: 1014/15 = 67.6

The mean is 67.6 km.

This value is exact and hasn't been rounded.

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For the median, we'll need to sort the values from smallest to largest.

The original data set is

51, 108, 40, 177, 56, 64, 32, 32, 72, 37, 64, 48, 121, 56, 56

The sorted data set is

32, 32, 37, 40, 48, 51, 56, 56, 56, 64, 64, 72, 108, 121, 177

Because the sample size n = 15 is odd, it means that the middle slot is found at slot 8 because of the scratch work: (n+1)/2 = (15+1)/2 = 8

The value in slot 8 is 56 (it's the 2nd copy of "56" to be exact)

This is the middle-most value, so it is the median.

The median is 56 km

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The mode is the most frequent value. In the sorted set, we can find the mode fairly quickly. In this case, the mode is 56 because it shows up the most times of any other number. It shows up 3 times, while the other values show up either 1 time or twice.

Here's a frequency table to help spot the mode more quickly. The mode is associated with the largest frequency.

`\begin{array}c \cline{1-2}\text{Value} & \text{Frequency}\\\cline{1-2}32 & 2\\\cline{1-2}37 & 1\\\cline{1-2}40 & 1\\\cline{1-2}48 & 1\\\cline{1-2}51 & 1\\\cline{1-2}56 & 3\\\cline{1-2}64 & 2\\\cline{1-2}72 & 1\\\cline{1-2}108 & 1\\\cline{1-2}121 & 1\\\cline{1-2}177 & 1\\\cline{1-2}\text{Total} & 15\\\cline{1-2}\end{array}`

Optionally, to help the mode stand out even more, we can sort the frequencies from largest to smallest like this

`\begin{array}c \cline{1-2}\text{Value} & \text{Frequency}\\\cline{1-2}56 & 3\\\cline{1-2}32 & 2\\\cline{1-2}64 & 2\\\cline{1-2}37 & 1\\\cline{1-2}40 & 1\\\cline{1-2}48 & 1\\\cline{1-2}51 & 1\\\cline{1-2}72 & 1\\\cline{1-2}108 & 1\\\cline{1-2}121 & 1\\\cline{1-2}177 & 1\\\cline{1-2}\text{Total} & 15\\\cline{1-2}\end{array}`

Spreadsheet software can quickly sort the values as I've described.

Side note: The median and mode won't always be equal to one another. This is just a coincidence.