Question

From the following data: Identify the data type, calculate appropriate descriptive statistics, draw a histogram to describe the data, and then verbally draw conclusions from the data.

Age	Age-Specific Rate	Case Count	Population
<1	29.4	1,168	3,975,414
1-4	23.0	3,665	15,937,085
5-9	13.4	2,746	20,481,130
10-14	15.1	3,112	20,605,579
15-19	24.0	5,061	21,084,710
20-24	35.5	8,052	22,693,026
25-29	60.2	13,475	22,401,168
30-34	97.6	21,090	21,617,533
35-39	144.5	29,350	20,312,646
40-44	228.4	46,048	20,156,736
45-49	354.7	73,790	20,801,156
50-54	566.5	126,274	22,289,734
55-59	828.6	180,368	21,767,855
60-64	1160.0	220,845	19,038,554
65-69	1574.2	252,650	16,049,246
70-74	1900.3	218,112	11,477,776
75-79	2129.8	172,938	8,119,847
80-84	2200.6	127,612	5,798,910
85+	2020.1	127,034	6,288,513

Answer 1

This is a discrete type data showing age-specific rates of a particular case(most likely death or a disease). Given under each age group we have corresponding population and the number of cases in that age group.

The age specific rates gives the number of occurrences of the case in 100,000 people of that age-group(Usually age groups consist of 5 year age groups)

Since the data consists of open end intervals, it is not possible to calculate the mean of the data. It is however logical to find the median age corresponding to age-specific rate. Other important statistics would be first quantile, third quantile, inter-quantile range,the mode and the age corresponding to minimum age-specific rate.

To calculate median we have to find out the cumulative frequencies and compare age corresponding to (N/2)th value. Which in this case is any age between 70-74.

Similarly to find first quantile or third quantile we have to find out age corresponding to (N/4)th value and (3*N/4)th value.

The mode of the data is age group 80-84.

The age corresponding to minimum age specific rate is 5-9.

Chart of Age-Specific Rate 2500 2000 1500 d 1000 500- Age

From the above bar graph and the descriptive statistics we can draw the following conclusions.

The age-specific rate is high in age group <1, and then decreases until age 10-14 where it is lowest. This rate then steadily increases until age 80-84 where it is highest. Again >85 it goes down a little since population under >85 is low and the number of cases is also low.