Question

1. an electric bill is an essential expense for young people who are living on their own. the following is a list of jordans monthly electric bills for the year ($115, $136, $144, $156, $99, $99, $99, $110, $130, $99)
2. what is the mean monthly electric bill?
3. what is the range?
4. what is the variance?
5. what is the standard deviation?

Explanation:

Step1: Calculate the mean

The data set is \(115, 136, 144, 156, 90, 90, 99, 110, 130, 95\). The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 10\) and \(\sum_{i=1}^{10}x_{i}=115 + 136+144+156+90+90+99+110+130+95=1165\). So \(\bar{x}=\frac{1165}{10}=116.5\).

Step2: Calculate the range

The range is the difference between the maximum and minimum values. The maximum value \(x_{max}=156\) and the minimum value \(x_{min}=90\). So the range \(R=x_{max}-x_{min}=156 - 90=66\).

Step3: Calculate the variance

The formula for the variance \(s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}\).
\((115-116.5)^{2}=(- 1.5)^{2}=2.25\), \((136 - 116.5)^{2}=19.5^{2}=380.25\), \((144-116.5)^{2}=27.5^{2}=756.25\), \((156-116.5)^{2}=39.5^{2}=1560.25\), \((90 - 116.5)^{2}=(-26.5)^{2}=702.25\), \((90-116.5)^{2}=(-26.5)^{2}=702.25\), \((99-116.5)^{2}=(-17.5)^{2}=306.25\), \((110-116.5)^{2}=(-6.5)^{2}=42.25\), \((130-116.5)^{2}=13.5^{2}=182.25\), \((95-116.5)^{2}=(-21.5)^{2}=462.25\).
\(\sum_{i = 1}^{10}(x_{i}-116.5)^{2}=2.25+380.25+756.25+1560.25+702.25+702.25+306.25+42.25+182.25+462.25 = 5194.5\).
\(s^{2}=\frac{5194.5}{9}\approx577.17\).

Step4: Calculate the standard - deviation

The standard - deviation \(s=\sqrt{s^{2}}\), so \(s=\sqrt{577.17}\approx24.02\).

Answer:

1. Mean: \(116.5\)
2. Range: \(66\)
3. Variance: approximately \(577.17\)
4. Standard deviation: approximately \(24.02\)