Question

Running times (Y) and maximal aerobic capacity (X) for 14 female Runners. Data collected for running times and maximal aerobic capacity are listed below X: 61.32 55.29 52.83 57.94 53.31 51.32 52.18 52.37 57.91 53.93 47.88 47.41 47.17 51.05 Y: 39.37 39.80 40.03 41.32 42.03 42.37 43.93 44.90 44.90 45.12 45.60 46.03 47.83 48.55 (a) Calculate the mean, median, MAD, MSD, and standard deviation for each variable. ? [Include all your steps and explain all the steps involved in details] (b) Which of these statistics give a measure of the center of data and which give a measure of the spread of data? [Explain in your own words] (c) Calculate the correlation of the two variables and pro-duce a scatterplot of Y against X. [Use excel for scatterplot, show all your computations concerning the correlation and explain all your steps] (d) Why is it inappropriate to calculate the autocorrelation of these data? [Explain in your own words] Note: It should be typed on Microsoft word including all the formula used.

Answer 1

(a)

From the data values,

	61.32	8.3264	69.3294	39.37	4.3286	18.7365
	55.29	2.2964	5.2736	39.8	3.8986	15.1989
	52.83	0.1636	0.0268	40.03	3.6686	13.4584
	57.94	4.9464	24.4672	41.32	2.3786	5.6576
	53.31	0.3164	0.1001	42.03	1.6686	2.7841
	51.32	1.6736	2.8008	42.37	1.3286	1.7651
	52.18	0.8136	0.6619	43.93	0.2314	0.0536
	52.37	0.6236	0.3888	44.9	1.2014	1.4434
	57.91	4.9164	24.1713	44.9	1.2014	1.4434
	53.93	0.9364	0.8769	45.12	1.4214	2.0205
	47.88	5.1136	26.1486	45.6	1.9014	3.6154
	47.41	5.5836	31.1763	46.03	2.3314	5.4356
	47.17	5.8236	33.9140	47.83	4.1314	17.0687
	51.05	1.9436	3.7775	48.55	4.8514	23.5364
Sum	741.91	43.4771	223.1131	611.78	34.5429	112.2176

For X

For Y

b)

Measure of the center: Mean

Measure of the spread: Mean Absolute Deviation (MAD), Mean Square Deviation (MSD) and Standard deviation (SD)

c)

The scatter plot is obtained in excel by following these steps,

Step 1: Write the data values in excel.

Step 2: Select the X and Y column then INSERT > Recommended Charts > Scatter > OK. The screenshot is shown below,

The correlation coefficient is obtained using the formula,

From the data values,

X	Y
61.32	39.37	8.3264	-4.3286	-36.0415	69.3294	18.7365
55.29	39.8	2.2964	-3.8986	-8.9528	5.2736	15.1989
52.83	40.03	-0.1636	-3.6686	0.6001	0.0268	13.4584
57.94	41.32	4.9464	-2.3786	-11.7654	24.4672	5.6576
53.31	42.03	0.3164	-1.6686	-0.5280	0.1001	2.7841
51.32	42.37	-1.6736	-1.3286	2.2235	2.8008	1.7651
52.18	43.93	-0.8136	0.2314	-0.1883	0.6619	0.0536
52.37	44.9	-0.6236	1.2014	-0.7492	0.3888	1.4434
57.91	44.9	4.9164	1.2014	5.9067	24.1713	1.4434
53.93	45.12	0.9364	1.4214	1.3311	0.8769	2.0205
47.88	45.6	-5.1136	1.9014	-9.7231	26.1486	3.6154
47.41	46.03	-5.5836	2.3314	-13.0177	31.1763	5.4356
47.17	47.83	-5.8236	4.1314	-24.0597	33.9140	17.0687
51.05	48.55	-1.9436	4.8514	-9.4291	3.7775	23.5364
Sum				-104.3934286	223.1131	112.2176

d)

Since X and Y are not time-series data, the auto-correlation can not be calculated.