Question

1. find the mean, median, mode and range of this data set: (3, 16, 4, 9, 7, 3, 9, 5) order your data 1st!!! mean:__ median: mode: range:__

Explanation:

Step1: Order the data set

$3,3,4,5,7,9,9,16$

Step2: Calculate the mean

The mean $\bar{x}=\frac{3 + 3+4+5+7+9+9+16}{8}=\frac{56}{8}=7$

Step3: Calculate the median

Since there are $n = 8$ (an even - numbered) data points, the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. $\frac{n}{2}=4$ and $\frac{n}{2}+1 = 5$. The 4th value is $5$ and the 5th value is $7$. So the median $=\frac{5 + 7}{2}=6$

Step4: Find the mode

The mode is the number that appears most frequently. Here, $3$ and $9$ both appear twice, so the modes are $3$ and $9$

Step5: Calculate the range

The range is the difference between the largest and the smallest values. Range $=16−3 = 13$

Answer:

Mean: $7$
Median: $6$
Mode: $3$ and $9$
Range: $13$