Statistics

Each question worth 10 points. Please show all work to receive full credits.

1. Consider the following data:

2,  7,  4,  4,  6,  1,  8,  15,  12,  7,  3,  16,  1,  2,  11,  5,  15,  4

1. Find the 5-number summary of the data.
2. Draw a box-and-whisker plot of the data

 

 

 

 

 

 

 

 

 

2. The mean time in a women’s 400-meter dash is 57.07 seconds, with a standard deviation of 1.05 seconds. What percent of women’s 400-meter dash is between 53.92 and 60.22?

 

 

 

 

3. Construct a frequency distribution and a frequency polygon for the data set below. Describe any patterns. In the table, include the midpoints, relative frequencies, and cumulative frequencies. Number of classes: 5

Exam Scores

Data set: Exam scores for all students in a statistics class.

 

83    92    94    82    73    98    78    85    72    90

89    92    96    89    75    85    63    47    75    82

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4. Consider the following 40 data points:

5   6   7   7   9   10  12  15  15  20

21  22  25  27  28  32  34  34  35  40

41  48  51  56  57  65  75  76  78  80

81  84  88  88  89  90  91  92  93  97

 

Find the percentiles P₃₁ and P₁₃   

 

 

 

 

 

 

 

 

5. ­­­­­­­­­­­­­­­­­­­­­­ The mean value of land and buildings per acre from a sample of farms is bell-shaped with a mean of $1750 and standard deviation of $350. Estimate the percent of farms whose land and building values per acre are between $700 and $2800.

 

 

 

 

 

 

 

 

 

6. The result of a random sample of the number of cars per household in region are show in the histogram. Estimate the sample mean and the sample standard deviation of the data set.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7. The data represent the air quality indices for 30 U.S. cities. Make a stem-and-leaf plot of the data set below.

25    35    20    75    10    10    61    89    44    22

34    33    38    30    47    53    44    57    71    20

42    52    48    41    35    59    53    61    65    25

 

 

 

 

 

 

 

 

8. Three adult males in the 20-29 age group are randomly selected. Their heights are 74 inches, 62 inches, and 80 inches. with a mean of 69.9 inches and standard deviation of 3.0 inches. Use z-scores to determine which heights, if any, are unusual.

 

 

 

 

 

 

 

 

 

9. The ages of the Supreme Court justices as of January 27, 2010 are listed. Find the population mean and the population standard deviation of the data.

55      89      73      73      61      76      71      59      55

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10. Average weight of newborn babies is bell-shaped with mean of 3325 grams and standard deviation of 571 grams. What percent of newborn babies weight between 2183 grams and 4467 grams?