Question

for each number set in this assignment, give the mean, median, mode, and range. if one of these quantities does not exist in the set, then put 0. 24, 40, 29, 33, 99, 86, 53, 53, 33

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data - points and $n$ is the number of data - points. Here, $n = 8$, and $\sum_{i=1}^{8}x_{i}=40 + 29+33 + 99+86+53+53+33=426$. So, $\bar{x}=\frac{426}{8}=53.25$.

Step2: Find the median

First, arrange the data in ascending order: $29,33,33,40,53,53,86,99$. Since $n = 8$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data - points. The $\frac{n}{2}=4$th value is $40$ and the $(\frac{n}{2}+1)=5$th value is $53$. So, the median $M=\frac{40 + 53}{2}=46.5$.

Step3: Determine the mode

The mode is the data - point that appears most frequently. In the set $\{40,29,33,99,86,53,53,33\}$, the numbers $33$ and $53$ both appear twice, and the other numbers appear only once. So, the modes are $33$ and $53$.

Step4: Calculate the range

The range $R$ is the difference between the largest and the smallest data - points. The largest value is $99$ and the smallest value is $29$. So, $R=99 - 29 = 70$.

Answer:

Mean: $53.25$
Median: $46.5$
Mode: $33,53$
Range: $70$