15.07.2022 - 06:34

A consumer watchdog organization is concerned about credit card debt. A survey of 10 young adults with credit card debt of more than $2,000 showed they paid an average of just over $100 per month agai

Question:

A consumer watchdog organization is concerned about credit card debt. A survey of 10 young adults with credit card debt of more than $2,000 showed they paid an average of just over $100 per month against their balances. Listed below are the amounts each young adult pad last month:

$110, $126, $103, $93, $99, $113, $87, $101, $109, $100

a. Compute the sample variance (Round your answer to 2 decimal places)

b. Determine the sample standard deviation (Round your answer to 2 decimal places.)

Answers (0)
  • Phyllis
    April 3, 2023 в 20:03
    a. The formula for sample variance is: s^2 = ?(x - x?)^2 / (n - 1) where ? is the sum of all the values, x is each individual value, x? is the mean, and n is the sample size. Using the given data, we can calculate the mean: x? = (110 + 126 + 103 + 93 + 99 + 113 + 87 + 101 + 109 + 100) / 10 = 105.1 Then, we can calculate the sum of the squared differences: ?(x - x?)^2 = (110 - 105.1)^2 + (126 - 105.1)^2 + (103 - 105.1)^2 + (93 - 105.1)^2 + (99 - 105.1)^2 + (113 - 105.1)^2 + (87 - 105.1)^2 + (101 - 105.1)^2 + (109 - 105.1)^2 + (100 - 105.1)^2 = 1746.78 Plugging these values into the formula for sample variance, we get: s^2 = 1746.78 / (10 - 1) = 194.09 Therefore, the sample variance is 194.09 (rounded to 2 decimal places). b. To find the sample standard deviation, we simply take the square root of the sample variance: s = ?(s^2) = ?194.09 = 13.93 Therefore, the sample standard deviation is 13.93 (rounded to 2 decimal places).
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