Question

Use the following vertical jump scores to develop a five category evaluation scale (Excellent = .88s and above, Good = .28 - .87s, etc.). Calculate the scores for each category (round to the nearest tenth) and the number of subjects that scored within each category. Round the mean and standard deviation to the nearest tenth. The vertical jump scores are as follows: 22, 28, 27.5, 25, 29, 25, 30, 24, 24, 24, 27.5, 32.5, 26, 23, 22.5, 29.5, 22.5, 25, 25, 35, 31.5, 27.5, 25.5, 22.5, 28.5, 27.

Mean _____
Standard Deviation _____

Grading Scale # of Students Receiving Grade
Excellent    ______ to ______    ______
Good    ______ to ______   ______
Average ______ to ______   ______
Fair ______ to ______   ______
Poor           ______ to ______   ______

Answer 1

The mean of the data sample is calculated as:

Mean = (22 + 28 + 27.5 + 25 + 29 + 25 + 30 + 24 + 24 + 24 + 27.5 + 32.5 + 26 + 23 + 22.5 + 29.5 + 22.5 + 25 + 25 + 35 + 31.5 + 27.5 + 25.5 + 22.5 + 28.5 + 27)/26
= 689.5/26
Mean = 26.5

and the standard deviation as;

Standard Deviation σ = √(1/26 - 1) x ((22 - 26.5192)² +..........................................+ ( 27 - 26.5192)²)

= √(1/25) x ((-4.5192)² + ......................................................... + (0.4808)²)

= √(0.04) x ((20.42316864) + .................................................. + (0.23116864))

= √(0.04) x (279.74038464)

= √(11.1896153856)

= 3.3451

= 3.3

The grading scale can be of any scale can be built as no specific scale is given, below is the grading scale where the digit value is the percentile score and the corresponding to the percentile score the Z score can be calculated using the Z table shown below, further using the Z score formula the scores that fall under the category can be calculated.

The Z score formula is :

Grading Scale no of Students Receiving Grade
Excellent : 0.80 to above
Good : 0.70 to 0.80
Average : 0. 60 to 0.70
Fair : 0.40 to 0.60
Poor : 0. 40 to below

The Z table that can be used to find the Z score, please see the marked value as an example for an Excellent grading scale for percentile more than 0.80.