Water scarcity has traditionally been a major concern in the Canary Islands. Water rights are divided into shares, which are privately owned. The article “The Social Construction of Scarcity. The Case of Water in Tenerife (Canary Islands)” discusses the extent to which many of the shares are concentrated among a few owners. The following table presents the number of owners who own various numbers of shares. (There were 15 owners who owned 50 shares or more; these are omitted.) Note that it is possible to own a fractional number of shares; for example, the interval 2–< 3 contains 112 individuals who owned at least 2 but less than 3 shares.

Question

a. Construct a histogram for these data.

b. Approximate the median number of shares owned by finding the point for which the areas on either side are equal.

c. Approximate the first quartile of the number of shares owned by finding the point for which 25% of the area is to the left.

d. Approximate the third quartile of the number of shares owned by finding the point for which 75% of the area is to the left.

Answer 1

(a)





(b) The sample size is 651, so the median is approximated by the point at which the area to the left is 0.5 = 325.5/651. The area to the left of 3 is 295/651, and the area to the left of 4 is 382/651. The point at which the area to the left is 325.5/651 is 3 + (325.5 – 295)?(382 – 295) = 3.35.

(c) The sample size is 651, so the first quartile is approximated by the point at which the area to the left is 0.25 = 162.75/651. The area to the left of 1 is 18/651, and the area to the left of 2 is 183/651. The point at which the area to the left is 162.75/651 is 1 + (162.75 – 18)?(183 – 18) = 1.88.

(d) The sample size is 651, so the third quartile is approximated by the point at which the area to the left is 0.75 = 488.25/651. The area to the left of 5 is 425/651, and the area to the left of 10 is 542/651. The point at which the area to the left is 488.25/651 is 5 + (10 – 5)(488.25 – 425)?(542 – 425) = 7.70.