EDUC7011 Lesson 21 - Introduction (Quantitative Variables)

Lesson 21: Univariate Descriptive Statistics for Quantitative Variables

Part 1: Combined (Men, Women) Analysis

Case Processing Summary
	Cases
	Valid		Missing		Total
	N	Percent	N	Percent	N	Percent
High School GPA Scores	90	100.0%	0	.0%	90	100.0%
College GPA Scores	90	100.0%	0	.0%	90	100.0%

Observation: 
There are a total of 90 participants in this survey, with each participant contributing one score to High School GPA and College GPA respectively.

 High School GPA Scores

Descriptives
			Statistic	Std. Error
High School GPA Scores	Mean		2.5379	.09175
	95% Confidence Interval for Mean	Lower Bound	2.3556
		Upper Bound	2.7202
	5% Trimmed Mean		2.5372
	Median		2.5350
	Variance		.758
	Std. Deviation		.87046
	Minimum		1.00
	Maximum		4.00
	Range		3.00
	Interquartile Range		1.26
	Skewness		.125	.254
	Kurtosis		-.889	.503

High School GPA Scores Stem-and-Leaf Plot

 Frequency    Stem &  Leaf

    14.00        1 .  00111122333334

    11.00        1 .  56677888999

    15.00        2 .  000000111222234

    22.00        2 .  5555555566666667789999

    11.00        3 .  00001111223

     9.00        3 .  555778889

     8.00        4 .  00000000

 Stem width:      1.00

 Each leaf:       1 case(s)

 College GPA Scores

Descriptives
			Statistic	Std. Error
College GPA Scores	Mean		2.4871	.04751
	95% Confidence Interval for Mean	Lower Bound	2.3927
		Upper Bound	2.5815
	5% Trimmed Mean		2.4930
	Median		2.5650
	Variance		.203
	Std. Deviation		.45071
	Minimum		1.17
	Maximum		3.45
	Range		2.28
	Interquartile Range		.62
	Skewness		-.235	.254
	Kurtosis		.012	.503

College GPA Scores Stem-and-Leaf Plot

 Frequency    Stem &  Leaf

     1.00 Extremes    (=<1.2)

     1.00        1 .  4

     8.00        1 .  57777899

    34.00        2 .  0000000011111122222233333334444444

    34.00        2 .  5555556666666666666777778888899999

    12.00        3 .  000001123334

 Stem width:      1.00

 Each leaf:       1 case(s)

Part 2: Split (Men, Women) Analysis

Case Processing Summary
	Gender	Cases
		Valid		Missing		Total
		N	Percent	N	Percent	N	Percent
College GPA Scores	Men	46	100.0%	0	.0%	46	100.0%
	Women	44	100.0%	0	.0%	44	100.0%
High School GPA Scores	Men	46	100.0%	0	.0%	46	100.0%
	Women	44	100.0%	0	.0%	44	100.0%

Observation: 

Of the 90 participants, 46 are men and 44 are women.

College GPA Scores
 

Descriptives
	Gender			Statistic	Std. Error
College GPA Scores	Men	Mean		2.2533	.05887
		95% Confidence Interval for Mean	Lower Bound	2.1347
			Upper Bound	2.3718
		5% Trimmed Mean		2.2679
		Median		2.2950
		Variance		.159
		Std. Deviation		.39929
		Minimum		1.17
		Maximum		2.94
		Range		1.77
		Interquartile Range		.60
		Skewness		-.446	.350
		Kurtosis		-.135	.688
	Women	Mean		2.7316	.05517
		95% Confidence Interval for Mean	Lower Bound	2.6203
			Upper Bound	2.8429
		5% Trimmed Mean		2.7307
		Median		2.6800
		Variance		.134
		Std. Deviation		.36598
		Minimum		2.05
		Maximum		3.45
		Range		1.40
		Interquartile Range		.58
		Skewness		.051	.357
		Kurtosis		-.744	.702

College GPA Scores Stem-and-Leaf Plot for gender= Men

 Frequency    Stem &  Leaf

     1.00        1 .  1

      .00        1 .

     2.00        1 .  45

     4.00        1 .  7777

     3.00        1 .  899

    11.00        2 .  00000011111

     8.00        2 .  22333333

     5.00        2 .  44455

     8.00        2 .  66666677

     4.00        2 .  8889

 Stem width:      1.00

 Each leaf:       1 case(s)

College GPA Scores Stem-and-Leaf Plot for gender= Women

 Frequency    Stem &  Leaf

     3.00        2 .  001

     5.00        2 .  22223

     8.00        2 .  44445555

    10.00        2 .  6666666777

     6.00        2 .  889999

     7.00        3 .  0000011

     4.00        3 .  2333

     1.00        3 .  4

 Stem width:      1.00

 Each leaf:       1 case(s)


 High School GPA Scores

Descriptives
		Gender				Statistic		Std. Error
	High School GPA Scores		Men	Mean			2.5276		.13596
				95% Confidence Interval for Mean	Lower Bound		2.2538
					Upper Bound		2.8015
				5% Trimmed Mean			2.5263
				Median			2.3800
				Variance			.850
				Std. Deviation			.92214
				Minimum			1.00
				Maximum			4.00
				Range			3.00
				Interquartile Range			1.57
				Skewness			.296		.350
				Kurtosis			-.996		.688
			Women	Mean			2.5486		.12415
				95% Confidence Interval for Mean	Lower Bound		2.2983
					Upper Bound		2.7990
				5% Trimmed Mean			2.5483
				Median			2.6200
				Variance			.678
				Std. Deviation			.82349
				Minimum			1.06
				Maximum			4.00
				Range			2.94
				Interquartile Range			1.12
				Skewness			-.113		.357
				Kurtosis			-.710		.702

 

High School GPA Scores Stem-and-Leaf Plot for gender= Men

 Frequency    Stem &  Leaf

     6.00        1 .  011123

     8.00        1 .  56778889

     9.00        2 .  000112222

     9.00        2 .  555556668

     3.00        3 .  023

     5.00        3 .  55788

     6.00        4 .  000000

 Stem width:      1.00

 Each leaf:       1 case(s)

High School GPA Scores Stem-and-Leaf Plot for gender= Women

 Frequency    Stem &  Leaf

     8.00        1 .  01233334

     3.00        1 .  699

     6.00        2 .  000134

    13.00        2 .  5556666779999

     8.00        3 .  00011112

     4.00        3 .  5789

     2.00        4 .  00

 Stem width:      1.00

 Each leaf:       1 case(s)

CONVERTing scores to Percentile Ranks (NOT assuming Normality)

College GPA: This is first ranked (Rank_CollGPA), followed by converting it into Percentile (PerRank_CollGPA) 

collgpa	gender	Rank_CollGPA	PerRank_CollGPA
1.75	1	6	6.67
1.48	1	2	2.22
2.65	2	59	65.56
2.57	2	47	52.22
2.93	2	75	83.33
2.59	2	50	55.56
2.61	2	52	57.78
2.67	2	62	68.89
2.64	2	58	64.44
3.03	2	80	88.89
3.07	2	82	91.11
2.64	1	58	64.44
1.71	1	4	4.44
2.32	1	32	35.56
2.26	1	29	32.22
2.8	1	69	76.67
2.34	1	33	36.67
2.37	1	36	40
2.64	1	58	64.44
2.05	1	15	16.67
2.57	2	47	52.22
2.94	1	77	85.56
2.93	2	75	83.33
2.74	1	65	72.22
2.32	1	32	35.56
2.81	1	70	77.78
2.1	1	20	22.22
2.15	1	22	24.44
2.85	1	72	80
1.17	1	1	1.11
2.08	2	18	20
2.36	2	34	37.78
2.25	2	28	31.11
2.94	2	77	85.56
3.09	2	83	92.22
2.62	2	54	60
2.01	1	12	13.33
2.46	2	42	46.67
3.03	2	80	88.89
3.34	2	88	97.78
2.18	1	23	25.56
2.64	1	58	64.44
2.6	1	51	56.67
2.37	1	36	40
2.13	1	21	23.33
2.95	2	78	86.67
2	1	11	12.22
2.05	1	15	16.67
2.19	2	24	26.67
1.91	1	9	10
2.44	2	40	44.44
2.1	1	20	22.22
1.84	1	8	8.89
2.06	1	17	18.89
2.45	2	41	45.56
2.72	2	64	71.11
2.06	1	17	18.89
2.24	2	27	30
2.05	2	15	16.67
2.75	2	67	74.44
3.13	2	84	93.33
2.48	1	44	48.89
2.47	1	43	47.78
3.06	2	81	90
2.58	2	48	53.33
2.2	2	25	27.78
2.82	2	71	78.89
2.79	2	68	75.56
2.22	2	26	28.89
2.56	1	45	50
2.75	1	67	74.44
3.31	2	87	96.67
2.59	1	50	55.56
3.37	2	89	98.89
2.67	1	62	68.89
2.44	2	40	44.44
2.69	2	63	70
2.86	2	73	81.11
1.58	1	3	3.33
1.79	1	7	7.78
1.75	1	6	6.67
2.62	1	54	60
3.14	2	85	94.44
3.45	2	90	100
1.94	1	10	11.11
2.41	1	38	42.22
2.27	1	30	33.33
3.25	2	86	95.56
2.66	2	60	66.67
2.38	1	37	41.11

After sorting (by Rank_CollGPA)
Note: Selected items were highlighted to check against data available in textbook

hsgpa	collgpa	gender	Rank_CollGPA	PerRank_CollGPA
2.64	1.17	1	1	1.11
1.87	1.48	1	2	2.22
1.85	1.58	1	3	3.33
1.77	1.71	1	4	4.44
4	1.75	1	6	6.67
2.26	1.75	1	6	6.67
1.54	1.79	1	7	7.78
2.21	1.84	1	8	8.89
3.21	1.91	1	9	10
2.62	1.94	1	10	11.11
1.69	2	1	11	12.22
2.24	2.01	1	12	13.33
4	2.05	1	15	16.67
2.07	2.05	1	15	16.67
1.44	2.05	2	15	16.67
1.29	2.06	1	17	18.89
4	2.06	1	17	18.89
3.02	2.08	2	18	20
4	2.1	1	20	22.22
1.32	2.1	1	20	22.22
2.2	2.13	1	21	23.33
2.18	2.15	1	22	24.44
3.5	2.18	1	23	25.56
2.62	2.19	2	24	26.67
1.32	2.2	2	25	27.78
2.59	2.22	2	26	28.89
3.15	2.24	2	27	30
3.19	2.25	2	28	31.11
1.83	2.26	1	29	32.22
3	2.27	1	30	33.33
1.17	2.32	1	32	35.56
1.19	2.32	1	32	35.56
3.79	2.34	1	33	36.67
1.24	2.36	2	34	37.78
2.04	2.37	1	36	40
2.81	2.37	1	36	40
3.86	2.38	1	37	41.11
2.5	2.41	1	38	42.22
1.06	2.44	2	40	44.44
2.74	2.44	2	40	44.44
3.99	2.45	2	41	45.56
4	2.46	2	42	46.67
1	2.47	1	43	47.78
2.61	2.48	1	44	48.89
4	2.56	1	45	50
1.31	2.57	2	47	52.22
2.11	2.57	2	47	52.22
2.3	2.58	2	48	53.33
1.91	2.59	2	50	55.56
2.08	2.59	1	50	55.56
3.38	2.6	1	51	56.67
3	2.61	2	52	57.78
2.95	2.62	2	54	60
2.53	2.62	1	54	60
2.92	2.64	2	58	64.44
1.78	2.64	1	58	64.44
3.5	2.64	1	58	64.44
4	2.64	1	58	64.44
3.85	2.65	2	59	65.56
3.19	2.66	2	60	66.67
2.95	2.67	2	62	68.89
1.99	2.67	1	62	68.89
2.92	2.69	2	63	70
2.44	2.72	2	64	71.11
2.59	2.74	1	65	72.22
2.54	2.75	2	67	74.44
2.52	2.75	1	67	74.44
3.5	2.79	2	68	75.56
1.13	2.8	1	69	76.67
2.14	2.81	1	70	77.78
3.1	2.82	2	71	78.89
2.5	2.85	1	72	80
4	2.86	2	73	81.11
2.62	2.93	2	75	83.33
2.62	2.93	2	75	83.33
3.87	2.94	1	77	85.56
2.09	2.94	2	77	85.56
2.04	2.95	2	78	86.67
2.74	3.03	2	80	88.89
3.78	3.03	2	80	88.89
1.93	3.06	2	81	90
2.07	3.07	2	82	91.11
3.22	3.09	2	83	92.22
1.36	3.13	2	84	93.33
1.39	3.14	2	85	94.44
2.5	3.25	2	86	95.56
1.69	3.31	2	87	96.67
1.12	3.34	2	88	97.78
2.62	3.37	2	89	98.89
3	3.45	2	90	100