# Business Statistics

## Statistics Review Measures, Box Plots Name ___________________

**Requirement for points: Work must be shown. Sketches must be shown.**

1. Use the following **sample** data to calculate the Measures of Central Tendency and Dispersion:

*Two decimal places.*

40 48 32 52 38 42

(x – ) | (x – )2 | |

Mean = Range =

Median = Variance =

Mode = Standard Deviation =

**2. Write the formulas for the mean for a sample AND for a population, using proper notation.**

**Write the formulas for the standard deviation for a sample AND for a population, using proper notation.**

**3. Sketch the **three approximate percentages** and their **corresponding number of standard deviations** for the Empirical Rule.**

**4. Data are drawn from a normal distribution with a mean of 80, standard deviation of 4**. **Use the Empirical Rule**. **SKETCH the values and the Z scores.**

a) Approximately what percentage of the observations fall between 68 and 92?

b) Approximately what percentage of the observations fall between 76 and 84?

c) Approximately what percentage of the observations are more than 84?

d) Approximately what percentage of the observations fall between 76 and 88?

**e) **What is the Z score for** **an observation of 85?

**f) **What is the x value (data value) when the Z score is +2.5?

**5.** **An average light bulb manufactured by the Acme Corporation lasts 300 days with a standard deviation of 50 days.**

**Use the Empirical Rule**. **SKETCH the values and the Z scores.**

a) Assuming that bulb life is normally distributed, what is the probability that a light bulb will last between 250 and 350 days?

b) How many days will approximately 95% of light bulbs last?

c) How many standard deviations from the mean is 465 days?

**6. The following data show the miles per gallon of small SUVs. Sketch a boxplot.**

12 9 27 15 68 35 21 32 22

Calculate the smallest, Q1, median, Q3, largest values, range, interquartile range, and identify any outliers for a box plot.

**7.** City Council has 9 members. The mayor is setting up a committee of 3 where one person will lead the committee, one person will record the meeting, one person will brief the mayor after the meeting. How many committee choices does the mayor have? **SHOW the math.**

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