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The following data points represent the volume of gas in each race car driver's tank (in liters). 4,5,13,? If the mean of the data set is 7L, find the missing volume of gas. L

The following data points represent the volume of gas in each race car driver's tank (in liters).\newline4,5,13,? 4,5,13, ? \newlineIf the mean of the data set is 7 L 7 \mathrm{~L} , find the missing volume of gas.\newlineL

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Full solution

Q. The following data points represent the volume of gas in each race car driver's tank (in liters).\newline4,5,13,? 4,5,13, ? \newlineIf the mean of the data set is 7 L 7 \mathrm{~L} , find the missing volume of gas.\newlineL
  1. Given Data Points: We are given the following data points for the volume of gas in each race car driver's tank: 44, 55, 1313, and an unknown value represented by ?? We are also given that the mean volume of gas is 77 liters. To find the missing volume, we will use the formula for the mean, which is the sum of all data points divided by the number of data points.
  2. Calculate Sum: First, let's calculate the sum of the given data points without the missing value: 4+5+13=224 + 5 + 13 = 22 liters.
  3. Total Sum Calculation: Since the mean is 77 liters and there are 44 data points including the missing value, the total sum of all data points should be 77 liters times 44 data points, which equals 2828 liters.
  4. Set Up Equation: Now, we can set up an equation to find the missing value (?). Let the missing value be represented by xx. The equation will be: 2222 (sum of known data points) + xx (missing value) = 2828 (total sum required for the mean to be 77 liters).
  5. Solve for Missing Value: Solving for xx, we get: x=28−22x = 28 - 22.
  6. Calculate Missing Value: Calculating the value of xx, we find that x=6x = 6 liters. This is the missing volume of gas needed for the mean of the data set to be 77 liters.

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