Question

1. calculate the mean, median, mode and range for the following data set: 15, 35, 50, 17, 33

mean: 30
median: 33
mode: no mode

Explanation:

Step 1: Calculate the mean

The mean $\bar{x}$ of a data - set $x_1,x_2,\cdots,x_n$ is given by $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here, $x_1 = 15,x_2 = 35,x_3 = 50,x_4 = 17,x_5 = 33$, and $n = 5$. Then $\sum_{i=1}^{5}x_i=15 + 35+50+17+33=150$. So, $\bar{x}=\frac{150}{5}=30$.

Step 2: Calculate the median

First, arrange the data - set in ascending order: $15,17,33,35,50$. Since $n = 5$ (an odd number), the median is the middle - value. The middle value is the third value when $n = 5$, so the median is $33$.

Step 3: Calculate the mode

The mode is the value that appears most frequently in the data - set. In the data - set $15,35,50,17,33$, each value appears only once. So, there is no mode.

Step 4: Calculate the range

The range is the difference between the maximum and minimum values in the data - set. The maximum value is $50$ and the minimum value is $15$. So, the range is $50 - 15=35$.

Answer:

Mean: 30
Median: 33
Mode: no mode
Range: 35