Question

(Question: Is the combined scores data approximately normal? Yes or no?)

Data:

Race	Position	Oral exam results	Written exam results	Combined results
B	Lieutenant	45.83	46	45.932
B	Lieutenant	52.92	49	50.568
B	Captain	54.76	49	51.304
H	Lieutenant	48.33	58	54.132
B	Lieutenant	52.08	56	54.432
H	Lieutenant	40.83	64	54.732
B	Captain	60	53	55.8
W	Captain	53.81	58	56.324
B	Lieutenant	58.75	55	56.5
W	Lieutenant	54.58	58	56.632
B	Lieutenant	55.83	58	57.132
W	Lieutenant	45.42	65	57.168
H	Lieutenant	44.17	66	57.268
H	Captain	42.86	67	57.344
W	Lieutenant	44.58	66	57.432
W	Lieutenant	51.25	62	57.7
W	Lieutenant	57.92	58	57.968
B	Captain	70.48	50	58.192
B	Lieutenant	60.83	58	59.132
H	Lieutenant	46.25	68	59.3
H	Captain	57.14	61	59.456
W	Lieutenant	60	60	60
W	Lieutenant	49.58	67	60.032
B	Lieutenant	51.25	66	60.1
B	Lieutenant	55	64	60.4
B	Captain	67.62	56	60.648
H	Lieutenant	51.25	67	60.7
H	Lieutenant	42.5	73	60.8
W	Captain	48.57	69	60.828
B	Lieutenant	56.25	64	60.9
B	Lieutenant	56.67	64	61.068
W	Lieutenant	56.25	66	62.1
H	Captain	58.57	65	62.428
H	Lieutenant	50.42	71	62.768
W	Lieutenant	71.67	57	62.868
W	Captain	55.24	68	62.896
H	Lieutenant	51.67	71	63.268
B	Lieutenant	69.17	60	63.668
H	Lieutenant	57.5	70	65
W	Lieutenant	50.42	75	65.168
B	Lieutenant	66.25	65	65.5
W	Lieutenant	55	73	65.8
H	Captain	67.14	65	65.856
H	Lieutenant	56.25	73	66.3
W	Lieutenant	79.17	59	67.068
B	Captain	52.38	77	67.152
W	Lieutenant	64.58	69	67.232
B	Lieutenant	70.83	65	67.332
W	Captain	57.14	75	67.856
W	Lieutenant	51.67	79	68.068
H	Lieutenant	62.5	72	68.2
W	Lieutenant	51.25	80	68.5
W	Lieutenant	73.75	66	69.1
W	Lieutenant	58.75	76	69.1
H	Lieutenant	70.83	68	69.132
H	Captain	60.48	75	69.192
W	Captain	59.05	76	69.22
W	Captain	71.43	68	69.372
W	Captain	71.43	68	69.372
W	Lieutenant	64.58	73	69.632
W	Captain	78.57	64	69.828
W	Captain	62.38	75	69.952
W	Lieutenant	71.67	69	70.068
W	Lieutenant	73.75	68	70.3
B	Captain	70.95	70	70.38
W	Lieutenant	77.5	66	70.6
H	Lieutenant	53.75	82	70.7
W	Lieutenant	65.83	74	70.732
W	Lieutenant	58.33	79	70.732
H	Lieutenant	69.17	72	70.868
H	Lieutenant	55	82	71.2
W	Captain	56.67	81	71.268
W	Captain	82.38	64	71.352
B	Captain	68.57	74	71.828
W	Lieutenant	73.33	71	71.932
W	Lieutenant	72.5	72	72.2
B	Lieutenant	92.08	59	72.232
W	Lieutenant	66.67	76	72.268
B	Lieutenant	70.83	74	72.732
W	Lieutenant	78.33	70	73.332
W	Captain	70	76	73.6
W	Captain	73.33	74	73.732
B	Lieutenant	65.83	80	74.332
W	Lieutenant	87.5	66	74.6
B	Captain	82.38	70	74.952
W	Captain	76.67	74	75.068
W	Lieutenant	63.33	83	75.132
W	Captain	73.81	77	75.724
W	Lieutenant	74.17	77	75.868
B	Lieutenant	80.42	73	75.968
H	Captain	79.05	74	76.02
B	Lieutenant	61.25	86	76.1
W	Captain	80	74	76.4
W	Captain	87.62	69	76.448
B	Lieutenant	77.5	76	76.6
W	Lieutenant	58.75	89	76.9
W	Captain	84.29	72	76.916
W	Lieutenant	73.75	81	78.1
W	Captain	73.81	81	78.124
H	Captain	70	84	78.4
W	Lieutenant	69.58	86	79.432
W	Captain	76.19	82	79.676
H	Captain	76.19	82	79.676
W	Captain	76.19	84	80.876
W	Captain	88.57	76	81.028
W	Lieutenant	68.33	91	81.932
W	Lieutenant	63.75	95	82.5
W	Lieutenant	80.83	84	82.732
W	Lieutenant	73.33	89	82.732
W	Lieutenant	73.75	91	84.1
W	Lieutenant	80	87	84.2
W	Lieutenant	85	84	84.4
W	Captain	82.38	87	85.152
W	Lieutenant	77.5	91	85.6
W	Lieutenant	87.5	87	87.2
W	Captain	80	95	89
W	Lieutenant	88.75	91	90.1
W	Captain	89.52	95	92.808

Answer 1

Yes. The combined scores data is approximately normal because the mean and median are close to each other; the median is almost equi-distant from Q3(upper quartile) and Q1(lower quartile).

It's mean =69.201

It's median =69.502

Total values, N =118

The following histogram and box plot indicate that the distribution of combined scores is approximately normal.