Question

1. find the mean, median, mode and range for the number of cars sold in the past 10 days. 1 7 3 0 5 7 3 6 7 8

a. mean: 4.7; median: 5.5; mode: 7; range: 8
b. mean: 4.7; median: 4; mode: 7; range: 8
c. mean: 4.7; median: 6; mode: 7; range: 8
d. mean: 4.7; median: 7; mode: 7; range: 8

Explanation:

Step1: Organize the data

First, we need to sort the data set: \(0, 1, 3, 3, 5, 6, 7, 7, 7, 8\) (the original data is \(1, 7, 3, 0, 5, 7, 3, 6, 7, 8\), after sorting).

Step2: Calculate the mean

The mean is calculated by the formula \(\text{Mean}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 10\) (number of data points) and \(x_{i}\) are the data values.
\(\sum_{i=1}^{10}x_{i}=0 + 1+3 + 3+5 + 6+7 + 7+7 + 8=47\)
\(\text{Mean}=\frac{47}{10}=4.7\)

Step3: Calculate the median

For \(n = 10\) (even number of data points), the median is the average of the \(\frac{n}{2}\)-th and \((\frac{n}{2}+ 1)\)-th values.
\(\frac{n}{2}=\frac{10}{2}=5\)-th value is \(5\), \((\frac{n}{2}+1)=6\)-th value is \(6\)
\(\text{Median}=\frac{5 + 6}{2}=\frac{11}{2}=5.5\)

Step4: Calculate the mode

The mode is the value that appears most frequently. In the sorted data, \(7\) appears \(3\) times, which is more than any other number. So mode \(= 7\).

Step5: Calculate the range

The range is the difference between the maximum and minimum values.
\(\text{Range}=\text{Max}-\text{Min}=8 - 0 = 8\)

Answer:

a. Mean: \(4.7\), median: \(5.5\); mode: \(7\); range: \(8\)