Question

question #9
find the mean of the following data set:
10, 20, 30, 40, 50, 60, 70, 80, 90
40
45
55
50

question #10
a set of data has the following frequency distribution. which measure of center
should be used to describe the center of the data?
14
12
10
8
6
4
2
0
mode
median
mean
range

Explanation:

Step1: Calculate the sum of the data set

The sum of the data set \(10 + 20+30 + 40+50+60+70+80+90=\sum_{i = 1}^{9}10i=10\times(1 + 2+\cdots+9)\).
Using the formula for the sum of the first \(n\) positive integers \(\sum_{k = 1}^{n}k=\frac{n(n + 1)}{2}\), with \(n = 9\), we have \(10\times\frac{9\times(9 + 1)}{2}=10\times45 = 450\).

Step2: Calculate the number of data points

The number of data points \(n=9\).

Step3: Calculate the mean

The mean formula is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). Substituting the values, \(\bar{x}=\frac{450}{9}=50\).

Answer:

\(50\)