Question

the ages of the members of a legislature from a particular state are listed below. find the mean, median, and mode of the data set, if possible. if any measure cannot be found or does not represent the center of the data, explain why.
65 42 34 44 55 44 36 50 45

Explanation:

Step1: Find the Mean

The mean is calculated by summing all the data points and dividing by the number of data points. First, sum the ages: \(65 + 42 + 34 + 44 + 55 + 44 + 36 + 50 + 45\). Let's calculate that: \(65+42 = 107\), \(107+34 = 141\), \(141+44 = 185\), \(185+55 = 240\), \(240+44 = 284\), \(284+36 = 320\), \(320+50 = 370\), \(370+45 = 415\). There are 9 data points. So the mean is \(\frac{415}{9}\approx46.11\).

Step2: Find the Median

To find the median, we first need to order the data set from least to greatest. The data set is: 34, 36, 42, 44, 44, 45, 50, 55, 65. There are 9 data points (an odd number), so the median is the middle value, which is the 5th value. The 5th value is 44.

Step3: Find the Mode

The mode is the value that appears most frequently. Looking at the data set, 44 appears twice, and all other values appear once. So the mode is 44.

Answer:

• Mean: \(\approx 46.11\)
• Median: \(44\)
• Mode: \(44\)