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.
  1. 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______

  1. 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 ____________

  1. 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.
  2. 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
  1. 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

  1. 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
  1. 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?
  1. 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?
  1. A z-score is:
  1. 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?
  1. 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?
  1. 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?
  1. 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?