Question

4.         Before the baby is born, John and Mary want to take a vacation to Gatlinburg, TN. They can travel in January or August. They do some research about the weather in January and in August in 2018. Using the information below answer the following questions.

Answer each of the following questions separately, showing all your work to reach each answer

A.        In which month was the difference between the mean high temperature and the mean low temperature smaller? Show all your calculations to support your answer.

B.        In which month was the difference between the median high temperature and the median low temperature larger? Show all your calculations to support your answer.

Day	High (°F)	Low (°F)
1 jan 2018	27.0	12.0
2 jan 2018	18.0	3.0
3 jan 2018	26.1	3.0
4 jan 2018	33.1	15.1
5 jan 2018	21.9	6.1
6 jan 2018	23.0	6.1
7 jan 2018	26.1	3.9
8 jan 2018	35.1	5.0
9 jan 2018	37.0	27.0
10 jan 2018	46.9	30.9
11 jan 2018	64.9	30.9
12 jan 2018	64.0	48.0
13 jan 2018	61.0	25.0
14 jan 2018	25.0	18.0
15 jan 2018	27.0	15.1
16 jan 2018	44.1	19.0
17 jan 2018	39.0	10.9
18 jan 2018	16.0	3.9
19 jan 2018	32.0	3.0
20 jan 2018	45.0	12.0
21 jan 2018	50.0	28.9
22 jan 2018	60.1	30.0
23 jan 2018	64.0	36.0
24 jan 2018	52.0	30.0
25 jan 2018	45.0	24.1
26 jan 2018	50.0	23.0
27 jan 2018	54.0	24.1
28 jan 2018	59.0	42.1
29 jan 2018	51.1	41.0
30 jan 2018	48.9	27.0
31 jan 2018	35.1	19.9

Day	High (°F)	Low (°F)
1 aug 2018	75.9	64.0
2 aug 2018	68.0	64.9
3 aug 2018	70.0	64.9
4 aug 2018	78.1	64.0
5 aug 2018	79.0	64.0
6 aug 2018	82.0	64.0
7 aug 2018	80.1	64.9
8 aug 2018	82.0	64.9
9 aug 2018	82.0	64.9
10 aug 2018	79.0	62.1
11 aug 2018	77.0	62.1
12 aug 2018	75.9	64.9
13 aug 2018	79.0	62.1
14 aug 2018	79.0	61.0
15 aug 2018	78.1	60.1
16 aug 2018	80.1	61.0
17 aug 2018	84.0	60.1
18 aug 2018	84.0	66.0
19 aug 2018	75.9	66.0
20 aug 2018	75.0	64.9
21 aug 2018	82.0	66.0
22 aug 2018	78.1	66.0
23 aug 2018	73.0	60.1
24 aug 2018	73.0	54.0
25 aug 2018	77.0	53.1
26 aug 2018	78.1	60.1
27 aug 2018	80.1	60.1
28 aug 2018	81.0	63.0
29 aug 2018	82.9	63.0
30 aug 2018	81.0	64.0
31 aug 2018	79.0	64.9

Answer 1

(a) The difference between the mean high temperature and the mean low temperature is smaller for August.

(b) The difference between the median high temperature and the median low temperature is larger for January.

Day	High	Low
	(°F)	(°F)	Difference			Mean
01-Jan-18	27	12	15		January	21.20645
02-Jan-18	18	3	15		August	15.61935
03-Jan-18	26.1	3	23.1
04-Jan-18	33.1	15.1	18			Median
05-Jan-18	21.9	6.1	15.8		January	21.1
06-Jan-18	23	6.1	16.9		August	16.9
07-Jan-18	26.1	3.9	22.2
08-Jan-18	35.1	5	30.1
09-Jan-18	37	27	10
10-Jan-18	46.9	30.9	16
11-Jan-18	64.9	30.9	34
12-Jan-18	64	48	16
13-Jan-18	61	25	36
14-Jan-18	25	18	7
15-Jan-18	27	15.1	11.9
16-Jan-18	44.1	19	25.1
17-Jan-18	39	10.9	28.1
18-Jan-18	16	3.9	12.1
19-Jan-18	32	3	29
20-Jan-18	45	12	33
21-Jan-18	50	28.9	21.1
22-Jan-18	60.1	30	30.1
23-Jan-18	64	36	28
24-Jan-18	52	30	22
25-Jan-18	45	24.1	20.9
26-Jan-18	50	23	27
27-Jan-18	54	24.1	29.9
28-Jan-18	59	42.1	16.9
29-Jan-18	51.1	41	10.1
30-Jan-18	48.9	27	21.9
31-Jan-18	35.1	19.9	15.2
Day	High	Low
	(°F)	(°F)
01 August 2018	75.9	64	11.9
02 August 2018	68	64.9	3.1
03 August 2018	70	64.9	5.1
04 August 2018	78.1	64	14.1
05 August 2018	79	64	15
06 August 2018	82	64	18
07 August 2018	80.1	64.9	15.2
08 August 2018	82	64.9	17.1
09 August 2018	82	64.9	17.1
10 August 2018	79	62.1	16.9
11 August 2018	77	62.1	14.9
12 August 2018	75.9	64.9	11
13 August 2018	79	62.1	16.9
14 August 2018	79	61	18
15 August 2018	78.1	60.1	18
16 August 2018	80.1	61	19.1
17 August 2018	84	60.1	23.9
18 August 2018	84	66	18
19 August 2018	75.9	66	9.9
20 August 2018	75	64.9	10.1
21 August 2018	82	66	16
22 August 2018	78.1	66	12.1
23 August 2018	73	60.1	12.9
24 August 2018	73	54	19
25 August 2018	77	53.1	23.9
26 August 2018	78.1	60.1	18
27 August 2018	80.1	60.1	20
28 August 2018	81	63	18
29 August 2018	82.9	63	19.9
30 August 2018	81	64	17
31 August 2018	79	64.9	14.1