Question

The output from a statistical software package indicates that the mean and standard deviation of a data set consisting of 400 measurements are ​$2,000 and ​$300​, respectively. a. What are the units of measurement of the variable of​ interest? A. Single measurements B. Units C. Dollars Your answer is correct. Based on the​ units, what type of data is​ this, quantitative or​ qualitative? The data is quantitative . b. What can be said about the number of measurements between ​$1,400 and ​$2,600​? That at least 3/4 of the measurements are between ​$1,400 and ​$2,600. What can be said about the number of measurements between ​$1,100 and ​$2,900​?

Answer 1

Answer:

a. What are the units of measurement of the variable of​ interest?

C. Dollars

Based on the​ units, what type of data is​ this, quantitative or​ qualitative?

The data is quantitative

b. What can be said about the number of measurements between ​$1,400 and ​$2,600​?

That at least 3/4 or 75% of the measurements are between ​$1,400 and ​$2,600.

c. What can be said about the number of measurements between ​$1,100 and ​$2,900​?

That at least 8/9 of the measurements are between ​$1,100 and ​$2,900

Step-by-step explanation:

a. What are the units of measurement of the variable of​ interest?

C. Dollars

Based on the​ units, what type of data is​ this, quantitative or​ qualitative?

Since the units is in dollars, therefore the data is quantitative.

b) We solve this question using Chebyshev's theorem.

Chebyshev's theorem states that:

1) At least 3/4 of the data lies within two standard deviations of the mean. This means, the interval endpoints :

Mean ± 2Standard deviation

2) At least 8/9 of the data lies within three standard deviations of the mean. This means, the interval endpoints :

Mean ± 3Standard deviation

For the given questions:

b. What can be said about the number of measurements between ​$1,400 and ​$2,600​?

Mean = $2000

Standard deviation = $300

We would apply the first rule of Chebyshev's theorem.

1) At least 3/4 of the data lies within two standard deviations of the mean. This means, the interval endpoints :

Mean ± 2Standard deviation

$2000 + 2($300)

$2000 + $600

= $2600

$2000 - 2($300)

= $2000 - $600

= $1400

For question b, the first rule of Chebyshev's theorem works.

Therefore, at least 3/4 of the measurements are between ​$1,400 and ​$2,600.

c. What can be said about the number of measurements between ​$1,100 and ​$2,900​?

Mean = $2000

Standard deviation = $300

We would apply the second rule of Chebyshev's theorem.

2) At least 8/9 of the data lies within two standard deviations of the mean. This means, the interval endpoints :

Mean ± 3Standard deviation

$2000 + 3($300)

$2000 + $900

= $2900

$2000 - 3($300)

= $2000 - $900

= $1100

For question c, the second rule of Chebyshev's theorem works.

Therefore, at least 8/9 of the measurements are between $1,100 and ​$2,900