Question

40 random college students were asked about their gender, age, height, weight, and ethnicity. The results were listed in the table below.

GENDER AGE HEIGHT (cm) WEIGHT (lb) ETHNICITY 1 M 18 165 175 Japanese 2 M 24 188 180 Chinese 3 M 19 190 200 Caucasian 4 M 19 192 200 Caucasian 5 M 18 175 160 Mixed 6 F 18 152 112 Japanese 7 F 18 152 120 Filipino 8 F 20 180 180 Mixed 9 F 21 172 190 Mixed 10 F 19 165 140 Filipino 11 F 20 160 140 Filipino 12 F 21 160 150 Caucasian 13 F 20 160 130 Caucasian 14 F 32 154 125 Japanese 15 F 44 128 90 Filipino 16 M 26 200 230 Mixed 17 M 20 190 180 Mixed 18 M 20 194 180 Chinese 19 M 19 180 195 Mixed 20 M 18 152 150 Caucasian 21 F 18 146 110 Japanese 22 F 19 150 125 Japanese 23 F 23 160 140 Mixed 24 F 20 154 135 Chinese 25 F 21 154 130 Japanese 26 F 20 172 175 Mixed 27 F 18 166 125 Chinese 28 F 19 168 130 Others 29 F 18 170 150 Others 30 F 19 156 160 Filipino 31 M 23 170 180 Mixed32 M 23 160 165 Japanese 33 M 23 168 150 Mixed 34 M 18 168 170 Mixed35 M 19 165 190 Filipino 36 M 21 162 165 Filipino 37 M 21 176 175 Caucasian 38 M 20 172 175 Caucasian 39 M 22 165 200 Mixed 40 M 18 165 150 Caucasian

1. Construct the frequency table for the height of male students using 5 number of classes.

2. Construct the frequency histogram for the height of male students and estimate the shape,

center, and variability of the distribution.

. Construct the OGIVE (Cumulative Frequency Polygon) for the height of male students and

indicate on the graph the position of the quartiles (Q1, Q2, Q3).

4. Construct the frequency table for the height of female students using 5 number of classes. 5. Construct the frequency histogram for the height of female students and estimate the shape,

center, and variability of the distribution. 6. Construct the OGIVE (Cumulative Frequency Polygon) for the height of female students and

indicate on the graph the position of the quartiles (Q1, Q2, Q3).

Answer 1

From the data specified, we cappture it in tabluar format (meaning rows and columns)

with rows being the data of 40 obs & column being gender, age, height, weight, and ethnicity\

1.

Some Vital information is needed to divide the data into classes

For males: Height of the class has following stats

mean	mode	median	min	max
174.85	165	171	152	200

Since it is specified we need to classify them in 5 classes

i.e we need to divide between difference of min and max such that they form 5 equally distributed non overlapping class

Frequency = no of times of occurence of individuals in a particular class

Height of class	frequency
150-160	2
161-170	8
171-180	4
181-190	3
191-200	3

Using EXCEL one can easily plot graph as below:

2.

Centre: Mean of the data = 174.85

Spread: Range of data = MAX-MIN= 48

Shape: We can see from graph that it is slightly left skewed with just one peak.

Variability: Since the bars are of different heights and do not look flat, hence considerable variability is seen.

ii) OGIVE

Plot of the upper class boundaries v/s cumulative frequency, with ogive begining from lower class boundary on horizontal axis.

Height of class	frequency	Class -boundaries	Cumulative frequency	Co-ordinates
150-160	2	149.5-160.5	2	(160.5,2)
161-170	8	160.5-170.5	10	(170.5,10)
171-180	4	170.5-180.5	14	(180.5,14)
181-190	3	180.5-190.5	17	(190.5,17)
191-200	3	190.5-200.5	20	(200.5,20)

Lower Quartile (Q1)	(N+1) * 1 / 4.
Middle Quartile (Q2)	(N+1) * 2 / 4.
Upper Quartile (Q3 )	(N+1) * 3 / 4.

Q1	Q2	Q3
5.25	10.5	15.75

4.

The same set of instruction repeats for female:

mean	mode	median	min	max
158.95	160	160	128	180

Height of class	frequency
128-139	1
139-150	2
151-161	10
162-172	6
173-183	1

5.

HISTOGRAM:

centre:- MEAN=158.95

spread:- RANGE=MAX-MIN=52

shape:- Symmetric

variability:- Bars are not flat or of same height throughout, hence there is sufficient variability.

6.

OGIVE:-

Height of class	frequency	Class -boundaries	Cumulative frequency	Co-ordinates
128-139	1	127.5-139.5	1	(139.5,1)
139-150	2	139.5-150.5	3	(150.5,2)
151-161	10	150.5-161.5	13	(161.5,10)
162-172	6	161.5-172.5	19	(172.5,6)
173-183	1	172.5-183.5	20	(183.5,1)

Lower Quartile (Q1)	(N+1) * 1 / 4.
Middle Quartile (Q2)	(N+1) * 2 / 4.
Upper Quartile (Q3 )	(N+1) * 3 / 4.

Q1	Q2	Q3
5.25	10.5	15.75