Question

83, 23, 24, 71, 52, 62, 63
mean:
median:
mode:
range:
23,24,52,62,63,71,83

Explanation:

Step1: Organize the data

First, we list the data set: \(23, 24, 52, 62, 63, 71, 83\) (sorted in ascending order).

Step2: Calculate the Mean

The mean is the sum of all values divided by the number of values.
Sum of values: \(23 + 24 + 52 + 62 + 63 + 71 + 83 = 378\)
Number of values: \(n = 7\)
Mean: \(\frac{378}{7} = 54\)

Step3: Calculate the Median

The median is the middle value when the data is sorted. For \(n = 7\) (odd), the median is the \(\frac{7 + 1}{2}= 4^{th}\) value.
Sorted data: \(23, 24, 52, 62, 63, 71, 83\)
\(4^{th}\) value is \(62\), so median is \(62\).

Step4: Determine the Mode

The mode is the value that appears most frequently. In this data set, all values appear once, so there is no mode (or we can say all values are modes, but typically we state no unique mode).

Step5: Calculate the Range

The range is the difference between the maximum and minimum values.
Maximum value: \(83\), Minimum value: \(23\)
Range: \(83 - 23 = 60\)

Answer:

• Mean: \(54\)
• Median: \(62\)
• Mode: No unique mode (all values occur once)
• Range: \(60\)