Question

The following are monthly expenditures of forty-four students on telephony cost in $. 2.1 Estimate the number of classes using Sturge's rule. 2.2 Estimate the width of class intervals using the range and the estimated number of classes.

Answer 1

Using Sturge's rule, we estimate that there are approximately 48 classes in the data. The width of each class interval, using the range and the estimated number of classes, is approximately $2.50.

Step-by-step explanation:

To estimate the number of classes using Sturge's rule, we first calculate the standard error of the mean (SE):

SE = standard deviation / sqrt(n)

where n is the number of students.

Next, we calculate the modified Sturge's formula:

k = 1 + 3.32 * log10(n/SE²)

where k is the estimated number of classes.

Using the given data, we first calculate the standard deviation:

standard deviation = sqrt(sum((x - mean)²)/(n-1)) = $1.88

Next, we calculate SE:

SE = $1.88 / sqrt(44) = $0.37

Finally, we calculate k:

k = 1 + 3.32 * log10(44/0.37²) = approximately 48 classes.

To estimate the width of each class interval, we first find the range:

range = maximum value - minimum value = $5.00 - $2.50 = $2.50.

Next, we divide the range by the estimated number of classes to find the width of each class interval:

width of each class interval = range / k = $2.50 / 48 = approximately $0.05 per class interval.