Exam 2: Methods for Describing Sets of Data

At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric. What percentage of the player's serves were between 115 mph and 145 mph?

A study was designed to investigate the effects of two variables - (1) a student's level of mathematical anxiety and (2) teaching method - on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 390 with a standard deviation of 30 on a standardized test. Assuming a non-mound-shaped distribution, what percentage of the students scored over 480?

The slices of a pie chart must be arranged from largest to smallest in a clockwise direction.

Various state and national automobile associations regularly survey gasoline stations to determine the current retail price of gasoline. Suppose one such national association contacts 200 stations in the United States to determine the price of regular unleaded gasoline at each station. In the context of this problem, define the following descriptive measures: $\mu , \sigma , \bar { x } , s$

Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean and standard deviation of the test scores are 76 and 4, respectively, and the distribution of scores is mound-shaped and symmetric. If a firm wanted to give the best 2.5% of the trainees a big promotion, what test score would be used to identify the trainees in question?

The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. 1 2 3 3 4 9 9 11 11 \ 11 14 14 19 22 23 24 25 29 a. Complete the class frequency table for the data. Total Medals Frequency 1-5 6-10 11-15 16-20 21-25 26-30 b. Using the classes from the frequency table, construct a histogram for the data.

In symmetric distributions, the mean and the median will be approximately equal.

What class percentage corresponds to a class relative frequency of .37?

The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. It was determined that the 75th percentile was the value $500. Which of the following interpretations of the 75th percentile is correct?

Calculate the variance of a sample for which $n = 5 , \sum x ^ { 2 } = 1320 , \quad \sum x = 80 .$

At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. If nothing is known about the shape of the distribution, what percentage of the player's serve speeds are less than 70 mph?

For any quantitative data set, $\sum ( x - \bar { x } ) = 0$

During one recent year, U.S. consumers redeemed 6.52 billion manufacturers' coupons and saved themselves $2.16 billion. Calculate and interpret the mean savings per coupon.

Suppose that 50 and 75 are two elements of a population data set and their z-scores are -3 and 2, respectively. Find the mean and standard deviation.

The total points scored by a basketball team for each game during its last season have been summarized in the table below. Score Frequency 41-60 3 61-80 8 81-100 12 101-120 7 a. Explain why you cannot use the information in the table to construct a stem-and-leaf display for the data. b. Construct a histogram for the scores.

The amount spent on textbooks for the fall term was recorded for a sample of five university students - $400, $350, $600, $525, and $450. Calculate the value of the sample mean for the data.

252 randomly sampled college students were asked, among other things, to estimate their college grade point average (GPA). The responses are shown in the stem-and-leaf plot shown below. Notice that a GPA of 3.65 would be indicated with a stem of 36 and a leaf of 5 in the plot. How many of the students who responded had GPA's that exceeded 3.55? Stem and Leaf Plot of GPA Leaf Digit Unit =0.01 Minimum 1.9900 199 represents 1.99 Median 3.1050 Maximum 4.0000 Stem Leaves 1 19 9 5 20 0668 6 21 0 11 22 05567 15 23 0113 20 24 00005 33 25 0000000000067 46 26 0000005577789 61 27 000000134455578 79 28 000000000144667799 88 29 002356777 116 30 0000000000000000000011344559 (19) 31 0000000000112235666 117 32 0000000000000000345568 95 33 000000000025557 80 34 0000000000000000333444566677889 49 35 000003355566677899 31 36 000005 25 37 022235588899 13 38 00002579 5 39 7 4 40 0000 252 cases included

Complete the frequency table for the data shown below. green blue brown orange blue brown orange blue red green blue brown green red brown blue brown blue blue red Color Frequency Green Blue Brown Orange

A histogram can be constructed using either class frequencies or class relative frequencies as the heights of the bars.

Test scores for a history class had a mean of 79 with a standard deviation of 4.5. Test scores for a physics class had a mean of 69 with a standard deviation of 3.7. One student earned a 55 on the history test and a 70 on the physics test. Calculate the z-score for each test. On which test did the student perform better?