2. an electric bill is an essential expense for young people who are living on their own. the following is a…

2. 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)\n1. what is the mean monthly electric bill?\n2. what is the range?\n3. what is the variance?\n4. what is the standard deviation?

2. 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)\n1. what is the mean monthly electric bill?\n2. what is the range?\n3. what is the variance?\n4. what is the standard deviation?

Answer

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)