Question

determine the sigma notation is and find the mean for problems 4-5. round to the nearest cent (2 decimal places).

1. the soccer team can’t decide where to have their end of year party. they have been able to get prices from the

following places:
bowling alley- $150, taco cart- $315, hot dog guy- $200, pizza place- $125, applebee’s- $300

sigma notation: _________________________

mean: ______________
side business of completing yard work. you research lawn mowers online and at

Explanation:

Step1: Identify the data points

Let the prices be \( x_1 = 150 \), \( x_2 = 315 \), \( x_3 = 200 \), \( x_4 = 125 \), \( x_5 = 300 \). There are \( n = 5 \) data points.

Step2: Write sigma notation

The sigma notation for the sum of these prices is \( \sum_{i = 1}^{5} x_i \), where \( x_i \) represents the price of the \( i \)-th venue.

Step3: Calculate the sum

First, find the sum of the prices:
\[

$$\begin{align*} \sum_{i = 1}^{5} x_i&= 150 + 315 + 200 + 125 + 300\\ &= 150+315 = 465; \quad 465 + 200 = 665; \quad 665 + 125 = 790; \quad 790 + 300 = 1090 \end{align*}$$

\]

Step4: Calculate the mean

The mean \( \bar{x} \) is given by the formula \( \bar{x}=\frac{\sum_{i = 1}^{n} x_i}{n} \). Substituting \( \sum_{i = 1}^{5} x_i = 1090 \) and \( n = 5 \):
\[
\bar{x}=\frac{1090}{5}=218.00
\]

Answer:

Sigma notation: \( \boldsymbol{\sum_{i = 1}^{5} x_i} \) (where \( x_i \) is the price of the \( i \)-th venue)
Mean: \( \boldsymbol{218.00} \) dollars