Question

6.2 measures of central tendency and spread. your grandfather wants to sell his antique 1932 ford. he begins to set his price by looking at ads and finds these prices: $24600, $19000, $33000, $15000, and $20000. calculate the mean, median, and range. mean: $ median: $ range: $ which would be the best measure (mean or median) to use to set the car price?

Explanation:

Step1: Calculate the mean

The mean formula is $\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here $n = 5$, and the data - points are $x_1=24600$, $x_2 = 19000$, $x_3=33000$, $x_4 = 15000$, $x_5=20000$.
$\sum_{i = 1}^{5}x_{i}=24600 + 19000+33000 + 15000+20000=111600$.
The mean $\bar{x}=\frac{111600}{5}=22320$.

Step2: Calculate the median

First, order the data: $15000,19000,20000,24600,33000$.
Since $n = 5$ (odd), the median is the middle - value. So the median is $20000$.

Step3: Calculate the range

The range formula is $R=\text{Max}-\text{Min}$. Here, $\text{Max}=33000$ and $\text{Min}=15000$. So the range $R = 33000-15000 = 18000$.

Step4: Decide the best measure

The mean is affected by the outlier ($33000$). The median is a better measure as it is not affected by extreme values.

Answer:

Mean: $\$22320$
Median: $\$20000$
Range: $\$18000$
Best measure: Median