MDM 4U
Chapter 3 Review: One variable statistics
1.What is the approximate range of a set of data that has been displayed in a histogram with 10 bars each with width 0.5?
2.Organize these traffic light waiting times (in seconds) into five uniform intervals, than construct a table with frequencies and cumulative frequencies:
6, / 11, / 14, / 12, / 16, / 25, / 21, / 24, / 17, / 19, / 20, / 2, / 14, / 11, / 83.The distribution of the ages of people at a Punctured Lung concert was mound-shaped with eighteen-year-olds representing the largest age group in attendance. Fred attended the concert with his ten-year-old son. Why did he not see many people near either of their ages at the Lung concert?
4.The final mark in a college statistics course is determined by taking the weighted mean of the marks in three categories: project, tests, and examination. The weight for the exam is 50, and the sum of all three weights is 100. Chris had a project mark of 75, a test mark of 80, an examination mark of 60, and a final mark of 68.5. What weight is given to the project?
5.Why is the mode, but not the mean or median an appropriate measure of central tendency for qualitative data?
6.Is it always true that the median equals ?
7.Explain how you find the interquartile range for a set of ungrouped data.
8.Find the standard deviation, to one decimal place, of the test marks tabulated below.
Mark / 41–50 / 51–60 / 61–70 / 71–80 / 81–90Frequency / 5 / 0 / 10 / 8 / 2
9.For what data sets is the following statement true?
If an additional datum, equal to the mean, is added to the set then the standard deviation will remain the same. Explain.
10.The masses of largemouth bass, in kilograms, are normally distributed with a mean of 1.1 and a standard deviation of 0.3. Any bass caught with a mass between 0.8 kg and 1.7 kg must be released. What percent of the bass does this represent?
11.The amount of barbeque sauce on Spicee Wings is normally distributed with a mean of 20 mL. What would you expect to find more of in a basket of these tasty morsels: wings with less than 19 mL of sauce or wings with more than 21 mL of sauce? Explain.
12.Suppose X~N(2, 32). Which set of data contains a greater percent of the data?
a) x 1 together with x 5 or b) 2 x 5?
13.How many flashlight batteries in a production run of 1500 will be rejected if only batteries between the 7th and 93rd percentile are accepted?
14.Hott Doggz have masses which are normally distributed. A Hott Dogg with a mass of 123.8 g determines the 90th percentile. A Hott Dogg with a mass of 124.4 g determines the 93rd percentile. Find the standard deviation of the masses of these succulent sausages, to one decimal place.
15.Use z-scores to determine who had a more disappointing quiz mark:
Alan had a mark of 8.5 on a quiz for which the mean mark was 10.1 and the standard deviation was 2.5. Belle had mark of 9.0 on a quiz for which the mean was 9.9 and the standard deviation was 1.5.
16.For X~N(, ), approximately 44% of the data are less than 2.9. Find the value of , to one decimal place.
17.In a certain U.S. college, incoming students have a mean GPA (Grade Point Average) of 2.57 with a standard deviation of 0.71. How many of the 850 new students have a GPA greater than 3.00 if the GPAs are normally distributed?
18.Why do normal z-score tables typically not include z values greater than 2.99?
19.The CPI for three consecutive months is given below.
January / February / March127.8 / 128.2 / 128.6
For a typical shopping basket item with a price of $1000 in January, which would be greater: its price increase from January to February or its price increase from February to March?