Question

key: 3 | 5 = 35
part a: find the mean of the data. show each step of work. (2 points)
part b: find the median of the data. explain how you determined the median. (2 points)
part c: find the mode of the data. explain how you determined the mode. (2 points)
part d: compare your values for mean, median, and mode from parts a, b, and c. which value would best represent the data, and why? explain using complete sentences. (4 points)

Explanation:

Part A:

Step1: List out all data values

From the stem - and - leaf plot, the data values are: \(35,42,46,51,57,68,74,75,85,86,95,98,98\)

Step2: Calculate the sum of data values

\(S=35 + 42+46+51+57+68+74+75+85+86+95+98+98\)
\(S = 910\)

Step3: Calculate the number of data values

\(n = 13\)

Step4: Calculate the mean

The mean formula is \(\bar{x}=\frac{S}{n}\). So \(\bar{x}=\frac{910}{13}=70\)

Part B:

Step1: Order the data (already ordered as \(35,42,46,51,57,68,74,75,85,86,95,98,98\))

Step2: Find the median position

For \(n = 13\) (odd), the median position is \(\frac{n + 1}{2}=\frac{13+1}{2}=7\)

Step3: Determine the median

The 7th value in the ordered list is \(74\). So the median is \(74\)

Part C:

Step1: Check the frequency of each value

The value \(98\) appears \(2\) times, and all other values appear only \(1\) time.

Step2: Determine the mode

Since \(98\) has the highest frequency, the mode is \(98\)

Part D:

The mean is \(70\), the median is \(74\), and the mode is \(98\). The median would best represent the data. The mean is affected by the relatively small value \(35\) and the relatively large values \(95,98,98\). The mode is an out - lier on the higher end. The median is less affected by extreme values and gives a better central tendency for this data set.

Answer:

• Part A: The mean is \(70\)
• Part B: The median is \(74\)
• Part C: The mode is \(98\)
• Part D: The median best represents the data as it is less affected by extreme values.