Question

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

1. 10, 71, 83, 97, 38, 55, 74, 5, 59, 97

Explanation:

Step1: Organize the data

First, we need to sort the data set in ascending order. The data set is \(10, 71, 83, 97, 38, 55, 74, 5, 59, 97\). Sorting it gives: \(5, 10, 38, 55, 59, 71, 74, 83, 97, 97\)

Step2: Calculate the Mean

The mean is calculated by summing all the values and dividing by the number of values.
Sum of the data: \(5 + 10 + 38 + 55 + 59 + 71 + 74 + 83 + 97 + 97\)
\(= 5+10 = 15\); \(15 + 38 = 53\); \(53 + 55 = 108\); \(108 + 59 = 167\); \(167 + 71 = 238\); \(238 + 74 = 312\); \(312 + 83 = 395\); \(395 + 97 = 492\); \(492 + 97 = 589\)
Number of values \(n = 10\)
Mean \(=\frac{589}{10}= 58.9\)

Step3: Calculate the Median

The median is the middle value of a sorted data set. Since \(n = 10\) (even number of 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 \(71\)
Median \(=\frac{59 + 71}{2}=\frac{130}{2}=65\)

Step4: Calculate the Mode

The mode is the value that appears most frequently. In the sorted data set \(5, 10, 38, 55, 59, 71, 74, 83, 97, 97\), the value \(97\) appears twice, and all other values appear once. So the mode is \(97\)

Step5: Calculate the Range

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

Answer:

• Mean: \(58.9\)
• Median: \(65\)
• Mode: \(97\)
• Range: \(92\)