Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

A study measures participants’ difficulty in walking on a scale from 0 to 5, whe

ID: 3340594 • Letter: A

Question

A study measures participants’ difficulty in walking on a scale from 0 to 5, where 0 means no difficulty walking and 5 means extreme difficulty walking. In this study, 93% of participants rated their difficulty walking as a 4 and 7% rated their difficulty walking as a 5 at the start of the study. (15 points)

(a)   What is the mean value for difficulty walking among participants in the study?

(b) What is the median value for difficulty walking?

(c)   What is the standard deviation for difficulty walking?

(d) After an exercise intervention, 10% of study participants report a 2-point decrease in difficulty walking (e.g., 5 to 3 or 4 to 2), 30% of study participants report a 1-point decrease in difficulty walking (e.g., 5 to 4 or 4 to 3) and 60% report no change. How will these changes affect the mean, median, and standard deviation?

                                                       i.     The mean will:

1.     Increase

2.     Decrease

3.     Stay the same

4.     Cannot Determine

                                                      ii.     The median will:

1.     Increase

2.     Decrease

3.     Stay the same

4.     Cannot Determine

                                                    iii.           The standard deviation will:

1.     Increase

2.     Decrease

3.     Stay the same

4.     Cannot Determine

Explanation / Answer

Solution- (a) Mean value = 0.93 * 4 + .07 *5

= 4.07

(b) Median value = middle value when data is arranged in ascending order.

As we know first 93% of values will be 4 and last 7% values would be 5.

Thus Middle value will be 4.

(c) E(X2) = .93 * 42 + .07 * 52

= 16.63

and variance = E(X2) - [ E(X) ]2

=.0651

So standard deviation = .0651^0.5

= 0.255

TY!