More Practice Practice Practice Problems … 1. Find the mean, mode, range and sta

Question

More Practice Practice Practice Problems …

1. Find the mean, mode, range and standard deviation of: 2, 2, 5, 5, 8, 2

2. Consider the stem and leaf below:

            3 | 2 4 5 5 6 7

            4 | 0 0 2 3

            5 | 1 1 1

            6 | 0 2

a. Give the 5 number summary.     B. Give the IQR      c. Comment on the shape

3. If P(Rain) = 0.73, P(not rain) = _____

4. If a data set is skewed to the right,
    then the median is ____________ (larger, smaller) than the mean.

5. What is the probability of getting a 1 or a 2 if a fair die is rolled? _____

6. What is the probability of getting a 1 and a 2 if a fair die is rolled? _____

7. The (mean, median) is not affected by outliers in a data set.

8. The mean score on a standardized test is 25 with a standard deviation of 5.
    What percentage of the data lies from 15 to 35. Assume the data is bell shaped.

9. consider the table by gender and diet program

                                    Weight Watchers       south beach (SB) a) Find P(female)

             Male    (M)              15                     25                    b) Find P (female | weight watchers)

                                                                                          c) Find P (male and South Beach)

            Female (F)                30                     10                     d) Find P(South Beach or female)

                                                                                                                e) Are “F” and “WW” independent?

Explanation / Answer

1. Mean=sumx/n=4

Mode=2, range=8-2=6 and sd=2.45

2. Max =62, Min=32, median=40, Q1=

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

32   34   35   35   36   37   40   40   42   43   51   51   51   60   62   

So, the bottom half is

32   34   35   35   36   37   40   

The median of these numbers is 35.

Q3=

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

32   34   35   35   36   37   40   40   42   43   51   51   51   60   62   

So, the upper half is

42   43   51   51   51   60   62   

The median of these numbers is 51.

b. IQR=The interquartile range = 51 - 35 = 16.

3. P(not rain)=1-0.73=0.27

4. Data skewed to right

mean > median > mode so answer is median is smaller than mean.

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