Statistics Review - Administration



Accelerated Math 2 Statistics Review

1. The salaries at a small business with 6 employees are as follows: $255,000, $32,000, $28,000, $24,000, $22,000, and $22,000. Find the mean, median, and mode of the salaries, explain which measures best represent a typical employee’s salary, and the reason why.

2. Given the following set of data, find the following measures of central tendency and spread. Then add 6 to each measurement and recalculate the measures of central tendency and spread of the revised measurements. How are the measures of central tendency changed? The measures of spread?

5, 12, 7, 14, 8, 9, 7

Mean________ ( _______ Mean_________ ( _______

Median_______ IQR______ Median_______ IQR ______

Mode________ Mode_________

3. Given the following set of test scores create a line plot for the set of data, find the mean and standard deviation. Then determine if the following data can be considered a normal distribution.

66, 75, 74, 78, 88, 99, 75, 88, 76, 74, 66, 89, 82, 92, 67, 89, 88, 84, 92, 65, 75, 85, 78, 79, 84, 94, 91, 81, 61, 79

Mean ________ (________

4. Ms. Gray’s 46 students had a mean score of 87 on the last test. Mr. Lamb’s 26 students had a mean score of 91. Find the mean score of all 72 students.

5. Make a frequency table and a histogram for the data set.

0.2, 1.3, 5.4, 4.3, 2.2, 4.3, 4.6, 3.5, 5.2, 4.8, 1.5, 3.7, 5.4, 4.0, 4.3, 5.2, 3.1, 2.9, 4.6, 4.8

|Frequency Table |

|Value |Frequency |

|0-1 |1 |

|1-2 |2 |

|2-3 |2 |

|3-4 |3 |

|4-5 |4 |

|5-6 |2 |

6. Create a box-and-whisker plot for the data set.

42, 45, 56, 48, 59, 60, 51, 54, 44, 51, 50, 44, 42, 49, 56

7. The table below lists the number of customers for a fast-food restaurant. Find the range and the standard deviation for the data.

|12375 |13890 |13202 |12825 |

|11982 |12098 |11829 |13234 |

|12025 |12502 |12654 |11723 |

8. Given a data set comprised of 5144 measurements that is bell shaped with a mean of 868. If 95% percent of the data lies between 854, and 882 then what is the standard deviation?

9. Given a group of data with mean 50 and standard deviation 6, at least what percent of the data will fall between 32 and 68?

10. A z-score is:

11. If a group of data has a mean of 80 and a standard deviation of 13.6, what is the raw score interval that should contain the lower 75% of the data?

12. Suppose the average score on a national test is 500 with a standard deviation of 100. If each score is increased by 25, what are the new mean and standard deviation?

13. In a certain southwestern city the air pollution index averages 62.5 during the year with a standard deviation of 18.0. Assuming that the empirical rule is appropriate, the index falls within what interval 95% (over the middle) of the time?

14. The average cost per ounce for glass cleaner is 7.7 cents with a standard deviation of 2.5 cents. What is the z-score of Windex with a cost of 10.1 cents per ounce?

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Mean = $ 63,833.33

Median = $ 26,000

Mode = $ 22,000

Median would represent best because of the outlier.

8.9

2.9

8

5

7

13

5

14

2.9

14.9

The measures of spread all remained the same but all the measures of central tendencies went up by 6.

80.5

9.5

70% within 1(, but 100% of the data within 2(. So this is probably not a normal distribution.

[pic]

( = 633.02

Range = 2167

868 + 2( = 882 or 868 – 2( = 854

So, ( = 7

50 + a(6) = 68 or 50 – a(6) = 32

a = 3 in either case

So, the % of the data within 3( is 99.7%

It is a way of comparing two unlike quantities by their relation to the mean. This is accomplished by scaling the distribution so the mean is 0 and each ( is worth 1.

[pic]

[pic]

Mean = 525

( = 100

[pic]

62.5 + 2(18) and 62.5 – 2(18)

[pic]

40

45

50

55

60

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