Question

An athletics trainer wants to measure the effectiveness of his training skills with a population of 63 athletes. He selects athletes by waiting at the training facility and pulling aside every third athlete to give him or her a questionnaire.

1. A specific question on the questionnaire asks about verbal coaching effectiveness on a 0-10 scale (0 = extremely confusing to 10 = extremely clear) with the following scores:

           

                        0, 9, 8, 8, 5, 4, 3, 2, 6, 5, 8, 1, 4, 10, 5, 8, 6, 7, 5, 4, 9

Calculate the mean, median, and mode of these scores. Which is the best measurement to report verbal coaching effectiveness? Why?

2. Calculate the variance and standard deviation of the sample. What conclusions about verbal coaching effectiveness can you make with this added information?

3. The trainer decided to change his method after the initial sample and then re-sampled his athletes (same sample method) to see if there was an improvement in his verbal coaching effectiveness score. The new average verbal coaching effectiveness score is 7.2 with a standard deviation of 2.2. What is the probability that a sample mean selected from this population would show no change (0) or a negative change (less than 0) after the new lectures were implemented?

Answer 1

Solution1:

Given scores

0, 9, 8, 8, 5, 4, 3, 2, 6, 5, 8, 1, 4, 10, 5, 8, 6, 7, 5, 4, 9

mean=sum of scores/total scores

=117/21

mean =5.571429

median is middlemost value after sorting data in ascending order(small to big)

Ascendng order is

0 1 2 3 4 4 4 5 5 5 5 6 6 7 8 8 8 8 9 9 10

median=5

mode is most repeating item

mode =5 as 5 repeats 4 times in data

median is the best measure as it is not affected by outliers.

Solution2:

x	xbar	x-xbar	(x-xbar)^2
0	5.571429	-5.571429	31.04082
9	5.571429	3.428571	11.7551
8	5.571429	2.428571	5.897957
8	5.571429	2.428571	5.897957
5	5.571429	-0.571429	0.326531
4	5.571429	-1.571429	2.469389
3	5.571429	-2.571429	6.612247
2	5.571429	-3.571429	12.75511
6	5.571429	0.428571	0.183673
5	5.571429	-0.571429	0.326531
8	5.571429	2.428571	5.897957
1	5.571429	-4.571429	20.89796
4	5.571429	-1.571429	2.469389
10	5.571429	4.428571	19.61224
5	5.571429	-0.571429	0.326531
8	5.571429	2.428571	5.897957
6	5.571429	0.428571	0.183673
7	5.571429	1.428571	2.040815
5	5.571429	-0.571429	0.326531
4	5.571429	-1.571429	2.469389
9	5.571429	3.428571	11.7551
		total	149.1429
xbar=mean=
		variance=149.1429/21-1
		variance=149.1429/20
		variance=7.457143

standard deviation=sqrt(variance)

=sqrt( 7.457143)

standard deviation =2.730777

mean=5.57

stddev=2.73

mean-sd=5.57-2.73=2.84

mean+sd=5.57+2.73=8.3

data is having less spread.

overall verbal coaching is effective