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------------------------------------------------ The distribution of the number of hours that a random sample of people spend doing chores per week is shown in the pie chart. Use 32 as the midpoint

for "30+ hours." Make a frequency distribution for the data. Then use the table to estimate the sample mean and the sample standard deviation of the

data set

Click the icon to view the pie chart

First construct the frequency distribution.

Class Frequency, f

0-4

5-9

10-14

15-19

20-24

25-29

30+

CIB

4

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Answer :

The frequency distribution for the given data is:

  • 0-4: 0.0349.
  • 5-9: 0.1512.
  • 10-14: 0.2558.
  • 15-19: 0.1977.
  • 20-24: 0.1628.
  • 25-29: 0.1512.
  • 30: 0.0465.

Treating the frequency distribution as a discrete distribution, we have that:

  • The mean is of 16.71.
  • The standard deviation is of 10.95.

What is the missing information?

The pie chart is missing, but is given at the end of the answer.

What is a relative frequency?

A relative frequency is given by the number of desired outcomes divided by the number of total outcomes.

A frequency distribution is composed by the relative frequencies of each outcome. From the pie chart, we have that there is a total of 3 + 13 + 22 + 17 + 14 + 13 + 4 = 86 people, hence the frequency distribution is given as follows:

  • 0-4: 3/86 = 0.0349.
  • 5-9: 13/86 = 0.1512.
  • 10-14: 22/86 = 0.2558.
  • 15-19: 17/86 = 0.1977.
  • 20-24: 14/86 = 0.1628.
  • 25-29: 13/86 = 0.1512.
  • 30: 4/86 = 0.0465.

What are the mean and the standard deviation of a discrete distribution?

  • The mean of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
  • The standard deviation of a discrete distribution is given by the square root of the sum of the differences squared between each observation and the mean, multiplied by their respective probabilities.

This is relevant because we want to treat the frequency distribution as a discrete distribution, taking the midpoint of each interval, hence:

  • P(X = 2): 0.0349.
  • P(X = 7): 0.1512.
  • P(X = 12): 0.2558.
  • P(X = 17): 0.1977.
  • P(X = 22): 0.1628.
  • P(X = 27): 0.1512.
  • P(X = 32): 0.0465.

Hence the mean is:

E(X) = 0.0349 x 2 + 0.1512 x 7 + 0.2558 x 12 + 0.1977 x 17 + 0.1628 x 22 + 0.1512 x 27 + 0.0465 x 32 = 16.71.

The mean is of 16.71.

The standard deviation is found as follows:

S(X) = sqrt[0.0349 x (2 - 16.71)² + 0.1512 x (7 - 16.71)² + 0.2558 x (12 - 16.71)² + 0.1977 x (17 - 16.71)² + 0.1628 x (22 - 16.71)² + 0.1512 x (27 - 16.71)² + 0.0465 x (32 - 16.71)²] = 10.95.

The standard deviation is of 10.95.

More can be learned about frequency distributions at https://brainly.com/question/1094036

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