Question

an auto dealers sales numbers are shown in the following table. find the mean, median, and mode prices of the cars they sold in may. (give your answers as whole numbers.) mean: $ median: $ 16000 mode: $

Explanation:

Step1: Calculate the total number of cars sold in May

The number of cars sold in May for each price: \(29\) (at \(\$19000\)), \(49\) (at \(\$16000\)), \(18\) (at \(\$13500\)).
Total number of cars \(n=29 + 49+18=96\)

Step2: Calculate the weighted - mean price

The formula for the weighted mean \(\bar{x}=\frac{\sum_{i = 1}^{k}x_{i}f_{i}}{\sum_{i = 1}^{k}f_{i}}\), where \(x_{i}\) is the price and \(f_{i}\) is the frequency.
\(\sum_{i = 1}^{k}x_{i}f_{i}=19000\times29 + 16000\times49+13500\times18\)
\(=19000\times29+16000\times49 + 13500\times18\)
\(=551000+784000 + 243000\)
\(=1578000\)
\(\bar{x}=\frac{1578000}{96}=16437.5\approx16438\)

Step3: Verify the median

The median is the middle - value. Since there are \(n = 96\) (an even number of data points), the median is the average of the \(\frac{n}{2}=48\)th and \((\frac{n}{2}+1) = 49\)th ordered data points.
When we order the data (based on the number of cars sold), the \(48\)th and \(49\)th values are in the group with price \(\$16000\)

Step4: Verify the mode

The mode is the value that appears most frequently. The number of cars sold at \(\$16000\) is \(49\), which is more than the number of cars sold at \(\$19000\) (\(29\)) and \(\$13500\) (\(18\))

Answer:

mean: \(\$16438\)
median: \(\$16000\)
mode: \(\$16000\)