Q1: Briefly explain the difference between ungrouped and grouped data. Give one example of each type of such data. Q2: The following data give the amounts of electric bills (rounded to the nearest dollar) for the past one month for 30 families. 75 38 55
34 41 42
47 63 35
26 55 39
56 61 45
29 73 71
48 61 24
42 76 47
33 46 67
67 51 52
a. Construct a frequency distribution table. Take 21 as the lower limit of the first class and 10 as the width of each class. b. Calculate the relative frequencies and percentages for all classes. c. What percentage of the families has a monthly electric bill of $61 or more? d. What percentage of the families has a monthly electric bill of $40 or less? e. Draw a histogram and a polygon for the relative frequency distribution. Ans : a. and b. Classes 21 to 30 31 to 40 41 to 50 51 to 60 61 to 70 71 to 80
Relative Frequency .100 .167 .267 .167 .167 .133
f 3 5 8 5 5 4
Percentage 10.0 16.7 26.7 16.7 16.7 13.3
c. 30.0% d. 26.7% Q3: The following data give the ages of 21 workers working for a large company. 41 63 55
54 48 61
22 67 47
28 47 59
31 58 36
39 37 48
58 26 54
a. Construct a frequency distribution table. Take the classes as 21 – 30, 31 – 40, 41 – 50, 51 – 60, and 61 – 70. b. Calculate the relative frequencies and percentages for all classes. c. What percentage of the workers are between 31 and 50 years of age? d. What percentage of the workers are 51 years of age or older? e. Draw a histogram and a polygon for the frequency distribution. Q4: The following data give the number of cars rented on each of the past 24 days at a car rental company. 12 31 9
8 22 17
18 19 29
25 32 23
33 37 31
25 28 33
15 18 25
26 30 23
Prepare a stem-and-leaf display. Arrange the leaves for each stem in increasing order.
Q5: An agency asked 60 people which of the five films nominated for Best Picture in 1997 should win the Oscar. Their responses appear in the following grouped data: Response The English Patient Fargo Jerry Maguire Secrets and Lies Shine Undecided/No Opinion Construct a bar graph and a pie chart to represent this data.
f 21 9 18 3 6 3