Cartogram. The following map, or cartogram, shows the distribution of the manufacture of boots and shoes in a certain year: The following cartogram shows the number of thousands of sheep in the United States in a certain year: CARTOGRAMS 1. Using the upper map on page 255, write the names of the states in which the manufacture of boots and shoes was $1000 and over per square mile in the year considered. 2. Give a reason for the concentration of boot and shoe manufacture in the states indicated in Ex. 1. 3. Using the lower map on page 255 write in order of number of sheep the names of the ten states having the largest numbers. 4. Write a statement in the way of a report to a shipping house as to the mean annual rainfall in inches, containing four important facts and based on the following cartogram: Such information is of great commercial importance, particularly to houses that sell goods which deteriorate quickly in a damp climate. 5. Sketch a map of your city or village and shade it to show approximately the areas occupied chiefly by stores, chiefly by manufacturing plants, and chiefly by residences. Curve-Line Graph. In many kinds of statistics the most convenient kind of graph is a curve-line graph. Such a line shows in a convenient form the changes from day to day or from year to year. 210 200 190 180 170 160 150 140 130 120 For example, a company that did a business of $103,000 in 1913, $105,000 in 1914, $110,000 in 1915, and $112,000 in 1916 found its business increased to $135,000 in 1917, $185,000 in 1918, and $208,000 in 1919. While these figures show a decided increase, we appreciate the sudden change more easily if we look at the graph. Such graphs are familiar to all readers of the newspapers and magazines of the present day, having become very common of late years. 110 100 13 14 15 16 17 18 19 20 Demand Curve. Curve-line graphs may be applied to the prices of goods, in which we may have a series of short straight lines connected to give the effect of a curve. 82¢ 24 16 c 200 400 600 800 For example, it was found in a certain market that when strawberries sold at 32¢ a quart, 25 qt. were sold daily; when the price dropped to 24¢, 100 qt. were sold daily; at 20¢, 300 qt. were sold; and so on, the average number of quarts sold per day being related to the price. The relation of price to sales may be indicated graphically as here shown, and the story is told much more vividly than by a mere recital of figures. We see at once that it is not always more profitable to sell at the highest prices, because the sales may be so small as to give but a small total profit. Such a graph is known as a demand curve, and commercial houses often find that a study of these curves is profitable in making their plans for purchasing stock. CURVE-LINE GRAPHS 1. Represent by a line graph the change in the average price of lake copper for six consecutive years, as follows: year A, 12.7¢; year B, 16.7¢; year C, 16.7¢; year D, 13.5¢ ; year E, 28¢; year F, 32 ¢. 2. The total annual sales of a grocery for a period of ten years were as follows: $16,000, $18,000, $20,000, $25,000, $24,000, $26,000, $28,000, $36,000, $43,000, $52,000. Draw a graph to show the trend of business. 3. From the graph in Ex. 2 estimate the probable amount of business the next year. Will it be advisable for the store to enlarge its plant and stock in this neighborhood? 4. Construct a demand curve based on the following facts which have been ascertained with respect to a certain article: 5. A grocer's records of sales of peaches for a certain year showed that he sold 10 baskets at $1.75 a basket; 30 baskets at $1.50; 70 baskets at $1.20; 80 baskets at $1.10; and 90 baskets at $1. Draw the demand curve and estimate the probable demand when the price is 90¢ a basket. 6. If the business of the grocer mentioned in Ex. 5 has increased 20% since last year, when the demand facts were recorded, draw a demand curve for this year, assuming that he will sell 20% more at each price mentioned above than he did last year. Using your curve as a guide, estimate how many baskets of peaches he will probably be able to sell this year at $1.45. CURVE-LINE GRAPHS 1. The distances of a train from its starting point in a run of 10 min. were measured and were found to be as follows: Minutes 1 2 Miles 3 4 5 6 78 9 10 0.2 0.5 0.9 1.5 2.2 3 3.8 4.6 5.1 5.5 Draw a graph and tell what it shows about the full speed. 2. The temperature at a certain school between 6 A. M. and 6 P.M. on the first day of last May was as shown by this graph. Write the approximate temperature for each hour and half hour of the day. 80 70° 60 50 6 8 10 12 2 4 6 3. The height of a plant in the schoolroom was measured on eight consecutive days in June and was found to be as follows: Day of the month 1 2 3 4 5 6 8 7 3.1 4.2 5.2 6.1 6.8 7.5 8.2 8.7 Draw a graph showing the growth, and from it determine in what part of the 7-day period it was growing the most rapidly. 4. In seven hours of a rainy day in April the amount of rain which fell was measured and was found to be as follows: Draw a graph showing the variation in rainfall by the hour. |