Statistics: Averages and Percentiles
Mean, median and mode, weighted and trimmed means, and reading percentiles.
15 questions, free, marked as you go with a worked explanation on every one.
What this covers
- averages
- math30 3 averages and percentiles
- normal distribution
The questions
- Seven service calls took 42, 47, 51, 51, 58, 63 and 70 minutes. What is the median time, in minutes?
- A course grade is made up of assignments worth 20%, quizzes worth 30% and a final exam worth 50%. A student averages 78 on assignments, 85 on quizzes and 72 on the final. What is the final grade, rounded to one decimal place?
- Seven daily sales figures are 4, 12, 14, 15, 16, 18 and 45 units. Calculate the trimmed mean by removing the highest and lowest values before averaging the rest.
- For those same seven sales figures (4, 12, 14, 15, 16, 18 and 45), what is the ordinary mean, rounded to one decimal place?
- A student's test score is at the 80th percentile of her class. What does this mean?
- In a class of 25 students, a score sits at the 80th percentile. Approximately how many students scored at or below that score?
- A small company's salaries are $38 000, $41 000, $43 000, $45 000 and $310 000 (the owner). Which measure best describes a typical employee's salary?
- Five machines recorded 3, 7, 7, 9 and 14 breakdowns last year. By how much does the mean exceed the mode?
- In a class of 40 students, a score at the 75th percentile means about how many students scored lower than that?
- Find the mode of: 22, 25, 22, 30, 22, 19.
- Find the range of: 102, 87, 145, 76, 110.
- Find the median of: 12, 18, 20, 25, 30, 40.
- A data set has a mean of 70 and a standard deviation of 8. Find the z-score for a value of 86.
- In a normal distribution, approximately what percent of values fall within 1 standard deviation of the mean?
- A data set has a mean of 50 and a standard deviation of 5. Find the raw value that corresponds to a z-score of -1.5.