Question

measures of center
find the mean, median, mode and range for each data set.

1. 2, 9, 7, 5, 2

mean\tmedian
mode\trange

1. 16, 21, 12, 15, 12, 21

mean\tmedian
mode\trange

Explanation:

1. For the data - set 2, 9, 7, 5, 2

Step1: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 5$ and $x_{1}=2,x_{2}=9,x_{3}=7,x_{4}=5,x_{5}=2$. So $\bar{x}=\frac{2 + 9+7 + 5+2}{5}=\frac{25}{5}=5$.

Step2: Calculate the median

First, order the data - set: 2, 2, 5, 7, 9. Since $n = 5$ (odd), the median is the middle - value, which is 5.

Step3: Calculate the mode

The mode is the number that appears most frequently. In the data - set 2, 9, 7, 5, 2, the number 2 appears twice and the other numbers appear once, so the mode is 2.

Step4: Calculate the range

The range is the difference between the maximum and minimum values. The maximum value is 9 and the minimum value is 2, so the range is $9 - 2=7$.

Step1: Calculate the mean

$n = 6$, and $\sum_{i = 1}^{6}x_{i}=16 + 21+12 + 15+12+21=97$. So the mean $\bar{x}=\frac{97}{6}\approx16.17$.

Step2: Calculate the median

Order the data - set: 12, 12, 15, 16, 21, 21. Since $n = 6$ (even), the median is the average of the two middle - values. The two middle - values are 15 and 16, so the median is $\frac{15 + 16}{2}=15.5$.

Step3: Calculate the mode

The numbers 12 and 21 both appear twice and the other numbers appear once, so the modes are 12 and 21.

Step4: Calculate the range

The maximum value is 21 and the minimum value is 12, so the range is $21 - 12 = 9$.

Answer:

Mean: 5
Median: 5
Mode: 2
Range: 7

2. For the data - set 16, 21, 12, 15, 12, 21