Question

A researcher wishes to conduct a study on differences in protein consumption by country of origin amongst immigrants in NYC. The researcher selects a sample of patients from the population of interest. The data below represents the ages of patients enrolled in the study.

52	52	63	55	33	47	71
48	30	52	45	52	40	55
67	57	45	43	49	45	45
38	44	46	53	58	61	44

!a. Construct the frequency distribution of patient ages. Group the data by 5’s, i.e. 20-24, 25-29, etc. Be sure to include frequency, percent, cumulative frequency, and cumulative percent.

1b. Calculate the following summary statistics: mean, variance, standard deviation, minimum, median, maximum, range. Show all work, and any formulas used.

. Create the following graphs from the data:

1c. Stem and Leaf Plot

1d. Histogram (with a bin width = 5)

1e. Pie Chart (group the ages by 10s, i.e. 20-29, 30-39, etc etc)

Answer 1

Part a)

Class Interval Frequency % frequency Cumulative frequency Cumulative % 30 - 34 2 0.07 (2/28) 2    0.07 (2/28) 35 - 39 1 0.04 (1/28) 3 (2+1) 0.11 (3/28) 40 - 44 4 0.14 (4/28) 7 (3+4) 0.25 (7/28) 45 - 49 8 0.29 15 (7+8) 0.54 50 - 54 5 0.18 20 0.71 55 - 59 4 0.14 24 0.86 60 - 64 2 0.07 26 0.93 65 - 69 1 0.04 27 0.96 70 - 74 1 0.04 28 1.00 Total 28

Minimum value = 30

Maximum Value = 71

Starting the class interval from 30 - 34, 35 - 39, 40 - 44.........so on.

Then count the values lies in the class interval for example:- between 30 - 34  

we have 30 & 33 whic lies between 30 - 34, so the frequency for the class interval 30-34 is 2

Similarly we can find the frequency for the other classes.

Part b) Calculate the following summary statistics

Mean = 1390 / 28 = 49.64

variance = = 2388.43 / 28 = 85.30

standard deviation = = = 9.24

minimum = Arrange the values in the ascending order, then find the lowest value = 30

maximum = 71

median = Is the middle most value, arrange the values in the ascending order

we have n = 28, so 14^th and 15^th value is the middle value of the data

48 & 49, taking average of it = (48 + 49) / 2 =48.5

Median = 48.5

Range = maximum - minimum = 71 - 30 = 41

Number	Values
1	30	385.84
2	33	276.98
3	38	135.56
4	40	92.98
5	43	44.13
6	44	31.84
7	44	31.84
8	45	21.56
9	45	21.56
10	45	21.56
11	45	21.56
12	46	13.27
13	47	6.98
14	48	2.70
15	49	0.41
16	52	5.56
17	52	5.56
18	52	5.56
19	52	5.56
20	53	11.27
21	55	28.70
22	55	28.70
23	57	54.13
24	58	69.84
25	61	128.98
26	63	178.41
27	67	301.27
28	71	456.13

Part C)  Stem and Leaf Plot

We have data values of two digit, consider the value of stem is at the tens place of data value and leaf value is the value at the ones place

First arrange the data in ascending order, keep adding the leaf value to the respective value of stem

for example :- consider the values 30,33,38 so stem value would be 3 and value for leaf would be 0 3 8 in similar way can calculate the values for the rest.

Stem	Leaf
0
1
2
3	0 3 8
4	0 3 4 4 5 5 5 5 6 7 8 9
5	2 2 2 2 3 5 5 7 8
6	1 3 7
7	1

Part d)

Class Interval	Frequency
30 - 34	2
35 - 39	1
40 - 44	4
45 - 49	8
50 - 54	5
55 - 59	4
60 - 64	2
65 - 69	1
70 - 74	1

Draw the histogram of the above table, take the frequency values on y axis ( Vertical axis) and lower class interval at x axis ( horizontal axis)

Part e) Pie Chart

Class Interval	Frequency
30 - 39	3
40 - 49	12
50 - 59	9
60 - 69	3
70 - 79	1