Describing data

1. Midland national bank selected a sample of 40 student checking accounts. Below are their end-of-month balances.

$404 $74 $234 $149 $149 $279
215 123 55 43 321 87
234 68 489 57 185 141
758 72 863 703 125 350
440 37 252 27 521 302
127 968 712 503 489 327
608 358 425 303 203

a. Tally the data into a frequency distribution using $100 as a class interval and $0 as the starting point.
b. Draw a cumulative frequency polygon
c. The bank considers any student with an ending balance of $400 or more a "preferred customer". Estimate the percentage of preferred customers.
d. The bank is also considering a service charge to the lowest 10% to the ending balances. What would you recommend as the cut-off point between those who have to pay a service charge and those who do not?

2) Merrill lynch recently completed a study regarding the size of online investments portfolios (stocks, bonds, mutual funds and certificate of deposit) for a sample of clients in the 40-50 yr old age groups. Listed following is the value of all the investments in thousands of dollars for the 70 participants in the study.

$669.9 $ 7.5 $77.2 $7.5 $125.7 $516.9
219.9 645.2 301.9 235.4 716.4 145.3
26.6 187.2 315.5 89.2 136.4 616.9
440.6 408.2 34.4 296.1 185.4 526.3
380.7 3.3 363.2 51.9 52.2 107.5
82.9 63.0 228.6 308.7 126.7 430.3
82.0 227.0 321.1 403.4 352.8 156.7
39.5 124.3 118.1 23.9 276.3 23.5
31.3 301.2 35.7 154.9 174.3 100.6
236.7 171.9 221.1 43.4 212.3 243.3
315.4 5.9 1,002.2 171.7 295.7 437.0
87.8 302.1 268.1 899.5
a. organize the data into frequency distribution. How many classes would you suggest? What value would you suggest for a class interval?

b. draw a histogram. Interpret your result.

3) Farming has changed from the early 1900s. In the early 20th century, machinery gradually replaced animal power. For e.g., in 1910 U.S. farms used 24.2 million horses and mules and only about 1,000 tractors. By 1960, 4.6 million tractors were used and only 3.2 million horses and mules. In 1920 there were only 60million farms in the United States. Today there are less than 2 million. Listed below is the number of farms, in thousands, for each of the 50 states. Write a paragraph summarizing your findings.

47 1 8 46 76 26 4 3 39 45
4 21 80 63 100 65 91 29 7 15
7 52 87 39 106 25 55 2 3 8
14 38 59 33 76 71 37 51 1 24
35 86 185 13 7 43 36 20 79 9