Question

for questions 1 through 3, find the mean, median, mode, and range for each set of data.

1. 10, 71, 83, 91, 38, 55, 74, 5, 59, 97
2. 769, 818, 824, 786, 751, 803, 769, 759, 201
3. 159, 109, 142, 64, 75, 70, 98, 130, 131, 72, 86

Explanation:

Step1: Organize the data

First, we list the data set: \(10, 71, 83, 91, 38, 55, 74, 5, 59, 97\). Then we sort it in ascending order: \(5, 10, 38, 55, 59, 71, 74, 83, 91, 97\).

Step2: Calculate the Mean

The mean is the sum of all values divided by the number of values. The sum \(S = 5 + 10 + 38 + 55 + 59 + 71 + 74 + 83 + 91 + 97\). Let's calculate \(S\):

$$
LATEXBLOCK0
$$

There are \(n = 10\) values. So the mean \(\bar{x}=\frac{S}{n}=\frac{583}{10} = 58.3\).

Step3: Calculate the Median

Since there are \(n = 10\) (even number) values, the median is the average of the \(\frac{n}{2}\)-th and \((\frac{n}{2}+ 1)\)-th values. \(\frac{n}{2}=5\) and \(\frac{n}{2}+ 1 = 6\). The 5th value is \(59\) and the 6th value is \(71\). So median \(=\frac{59 + 71}{2}=\frac{130}{2}=65\).

Step4: Calculate the Mode

The mode is the value that appears most frequently. In this data set, all values appear only once, so there is no mode (or we can say all values are modes with frequency 1).

Step5: Calculate the Range

The range is the difference between the maximum and minimum values. Maximum value \(= 97\), minimum value \(= 5\). So range \(=97 - 5=92\).

Answer:

• Mean: \(58.3\)
• Median: \(65\)
• Mode: No mode (or all values with frequency 1)
• Range: \(92\)