# statistics practice set week 1

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Practice Set 1

**Practice Set 1**

1. The following table lists the number of deaths by cause as reported by the Centers for Disease Control and Prevention on February 6, 2015:

a) What is the variable for this data set (use words)?

b) How many observations are in this data set (numeral)?

c) How many elements does this data set contain (numeral)?

2. Indicate which of the following variables are quantitative and which are qualitative.

Note: Spell quantitative and qualitative in lower case letters.

a) The amount of time a student spent studying for an exam

b) The amount of rain last year in 30 cities

c) The arrival status of an airline flight (early, on time, late, canceled) at an airport

d) A person’s blood type

e) The amount of gasoline put into a car at a gas station

3. A local gas station collected data from the day’s receipts, recording the gallons of gasoline each customer purchased. The following table lists the frequency distribution of the gallons of gas purchased by all customers on this one day at this gas station.

a) How many customers were served on this day at this gas station?

b) Find the class midpoints. Do all of the classes have the same width? If so, what is this width? If not, what are the different class widths?

c) What percentage of the customers purchased between 4 and 12 gallons? (do not include % sign. Round numerical value to one decimal place)

4. The following data give the one-way commuting times (in minutes) from home to work for a random sample of 50 workers.

23

17

34

26

18

33

46

42

12

37

44

15

22

19

28

32

18

39

40

48

16

11

9

24

18

26

31

7

30

15

18

22

29

32

30

21

19

14

26

37

25

36

23

39

42

46

29

17

24

31

- What is the frequency for each class 0–9, 10–19, 20–29, 30–39, and 40–49.
- Calculate the relative frequency and percentage for each class.
- What percentage of the workers in this sample commute for 30 minutes or more?

Note: Round relative frequency to two decimal places. Complete the table by calculating the frequency, relative frequency, and percentage.

5. The following data give the number of text messages sent on 40 randomly selected days during 2015 by a high school student.

32

33

33

34

35

36

37

37

37

37

38

39

40

41

41

42

42

42

43

44

44

45

45

45

47

47

47

47

47

48

48

49

50

50

51

52

53

54

59

61

Each stem has been displayed (left column). Complete this stem-and-leaf display for these data.

Note: Use a space in between each leaf. For example 1 2 3 4 5 6 7 8 9 (do not use this format 123456789).

6 A) Which of the five measures of center (the mean, the median, the trimmed mean, the weighted mean, and the mode) can be calculated for quantitative data only.

B) Which can be calculated for both quantitative and qualitative data?

7. Prices of cars have a distribution that is skewed to the right with outliers in the right tail. Which of the measures of center is the best to summarize this data set?

8. The following data give the amounts (in dollars) of electric bills for November 2015 for 12 randomly selected households selected from a small town.

Calculate the (a) mean, (b) median and (c) Is there a mode (Yes or No)?

9. The following data give the prices of seven textbooks randomly selected from a university bookstore.

$89

$170

$104

$113

$56

$161

$147

a) Find the mean for these data (input the numerical value without the dollar sign). Calculate the deviations of the data values from the mean.

b) Is the sum of these deviations zero (yes or no)?

c) Calculate the range (do not include unit).

d) Calculate the variance.

e) Calculate the standard deviation (round to one decimal place).

10. The following data give the speeds of 13 cars (in mph) measured by radar, traveling on I-84.

73

75

69

68

78

69

74

76

72

79

68

77

71

a) Find the values of the three quartiles and the interquartile range.

b) Calculate the (approximate) value of the 35th percentile (round to two decimal places).

c) Compute the percentile rank of 71 (round to two decimal places. Do not include the % symbol).

Note: Round to two decimal places. Do not include unit.

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