Question

A data set has a mean of 112 and a standard deviation of 2.5.

What is the margin of error for this data set?


A. 224


B. 5


C. 56


D. 1.25

Answer 1

Answer with explanation:

Mean of the data set
`\mu` = 112

Standard Deviation of the data set
`\sigma` =2.5

Since , 50% of data lies on both side of the mean.

Z at 50% = 0.1915

Margin of error for this data set

`=Z_{50 \text{percent}}*(\sigma)/(√(\mu))\\\\=0.1915 * (2.5)/(√(112))\\\\=0.1915 * (2.5)/(10.58)\\\\=0.1915 * 0.2362\\\\=0.0452`

Margin of error=0.045(approx)

Answer 2

The margin of error for this data set is option B )5

Explanation:

Given that a data set has a mean of 112 and a std deviation of 2.5

Since confidence interval level is not given, we can take it as 95% normally used much in finding margin of errors.

For 95% confidence interval, Z critical value is 1.96 or approximately 2.

Margin of error = Z critical * std deviation

= 2(2.5)

=5

Hence option B would b the right answer

The margin of error for this data set is option B )5