Question

The following data are the response times in seconds for n = 25 first graders to arrange three objects by size. 

(a) Find the mean and the standard deviation for these 25 response times. (Round your standard deviation to three decimal places.) 

(b) Order the data from smallest to largest. (Enter your answers as a comma-separated list.) 

(c) Find the z-scores for the smallest and largest response times. (Round your answers to two decimal places.) 

Is there any reason to believe that these times are unusually large or small? Explain. 

• Since neither of the z- unusually large or small. scores are greater than 3 in absolute value, the measurements are not judged to be unusually large or small.

• Since the z-score of the smallest value is greater than 3 in absolute value, the smallest value is unusually small. The largest value is not unusual. 

• Since the z-score of the largest value is greater than 3 in absolute value, the largest value is unusually large. The smallest value is not unusual. 

• Since both z-scores are greater than 3 in absolute value, the measurements are judged to be unusual.

Answer 1

(a) Let us get started with Mean,

since there are total 25 responses i.e. (n = 25)

and Formula for Mean:    =

= =  

Now, proceeding to standard deviation :

and Standard Deviation is equal to Square root of variance .i.e.

and

  

Now,

(b) Ordered List :

2.4, 2.9, 3.0, 3.5, 3.6, 3.7, 3.8, 3.9, 3.9, 3.9, 4.0, 4.1, 4.2, 4.2, 4.2, 4.3, 4.5, 4.5, 4.8, 4.9, 5.0, 5.2, 5.4, 5.5

(c) Now. obtaining Z-scores ;

Lowest Z-Score = = =

here, because it is the smallest number in the data.

Largest Z - score = =

here , because it is the largest number in the data.

Since, neither of the Z- scores are greater than 3 in absolute value, the measurements are not judged to be unusually large or small

because if it exceeds to 3 it would be quiet large then we can not say it is usually large or small. then it should be measured or regarded to be unusually large or small .