Graphs of Statistics

Graphs of statistics

Scientific data and business statistics are often shown by graphs. Sometimes the graph is a smooth curve; sometimes it is an irregular line made of straight pieces. To construct one, choose a scale for each axis, plot a point for each pair of numbers in the table, and connect the points.

Life insurance

The annual payment needed to insure a man's life for $1000:

Age	21	25	30	35	40	45
Payment	$18.40	$20.14	$22.14	$26.35	$30.94	$37.08

Age	50	55	60	65	70
Payment	$45.45	$56.93	$72.83	$95.14	$126.66

A river bed

Depths in feet at points 50 feet apart in a straight line across a river:

Feet from bank	0	100	200	300	400	500	600	700	800	900	1000
Depth (ft)	0.0	4.1	8.8	15.1	14.9	9.8	6.9	5.3	3.4	1.5	0.0

Feet from bank	50	150	250	350	450	550	650	750	850	950
Depth (ft)	2.2	6.4	12.0	16.3	13.0	8.0	5.7	5.0	2.0	1.0

Survivors

Starting with 100,000 persons at the age of 10, the number still living at later ages:

Age	10	15	20	25	30	35	40	45	50
Living	100,000	96,285	92,637	89,032	85,441	81,822	78,106	74,173	69,804

Age	55	60	65	70	75	80	85	90	95
Living	64,563	57,917	49,341	38,569	26,237	14,474	5,485	847	3

The public debt

The public debt of the United States at five-year intervals, in millions of dollars:

Year	1860	1865	1870	1875	1880
Millions	64	2,680	2,480	2,232	2,128

Year	1885	1890	1895	1900	1905
Millions	1,872	1,549	1,717	2,132	2,293

Wheat

The wheat crop of the United States, in millions of bushels:

Year	1892	1893	1894	1895	1896	1897	1898	1899	1900
Millions of bu.	399	515	396	460	467	427	530	675	547

Year	1901	1902	1903	1904	1905	1906	1907	1908
Millions of bu.	522	748	670	637	552	692	735	634

The book asks you to construct each of these graphs yourself (for instance, one inch for 5 years and one inch for $20 on the insurance graph). Try one on paper, then use the graphs above for the questions.

To read a value between two plotted points, assume the line runs straight from one to the next. For example, the payment at 52 is about 45.45 + \frac25(56.93 - 45.45) \approx 50.04 dollars.

Try one:

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Quick check

From the wheat table, by how many million bushels did the crop rise from 1901 to 1902?

Exercises

0 of 5 solved

How to type math

Use ^ for powers (a^2), / for fractions ((a+b)/2), sqrt(x) for square roots, and cbrt(x) for cube roots. You can leave out the multiplication sign: 3ab means 3 \cdot a \cdot b. Mixed numbers like 4 1/2 work too. The preview under each box shows how your answer was read.

These questions use the statistical graphs above. Readings from a curve are approximate; answers close to the graph's value are accepted.

A healthy man 21 years old can insure his life with a certain company for $1000 by making an annual payment of $18.40. The payments at other ages are given in the table and graph above. (The book asks you to draw the curve with one inch for 5 years and one inch for $20.) From the graph, at about what age does the payment reach $50? How much more is the payment at 60 than at 30?

The depths of a river at points 50 feet apart in a straight line across it are given in the table and the profile above. What is the greatest depth, and how far from the first bank is it? How wide is the river along this line?

Starting with 100,000 persons at the age of 10, the number still living at later ages is given in the table and graph above. At about what age are half of them (50,000) still living? How many die between the ages of 70 and 80?

The public debt of the United States at five-year intervals from 1860 to 1905 is given in the table and graph above, in millions of dollars. In which of these years was it greatest? By how many millions did it fall from 1865 to 1890? Between which two years shown did it rise the most? (Give the first year.)

The number of bushels of wheat produced in the United States each year from 1892 to 1908 is given in the table and graph above. In which year was the crop largest? smallest? In how many of these years was it over 600 million bushels?