Question

4. The following frequency table shows the test score distribution for a random sample of 25 students taking an introductory statistics class at a certain college. a. Find the missing relative frequency b. How many students in the sample RelativeF 0.08 0.04 Score 30-40 41-51 52-62 63-73 74 -84 85-95 had a score of at least 63? Total number of students taking an introductory statistics class at this college is 800. Based on the sample data above, estimate the total number students (in all intro to stats classes) who scored 52-84 on the test. c. 0.24 0.20 0.32 5. A frequency distribution for the ages of randomly selected 27 students taking a statistics course in a college is given below Age re 19 20 21 23 24 25 26 a. Make a relative frequency histogram for the data. Label axes and units. b. What is the shape of the distribution? c. Compute the sample mean 0 d. Use information from (c) to fill in the blanks in the following statement: In the sample of 27 students taking statistics, the average age of a student is about e. Do you agree with the following statement? Based on the sample data, we can infer that the average age of students taking a statistics course in a college is no greater than 21." Choose the best answer belo w: Yes, because the data came from a representative sample. No, because the sample is not representative of the population. No, because sample mean is different from the population mean. Consider the following data set consisting of test scores of students in a math class: 31, 33, 35, 36, 40,40,4,43,45, 47, 48, 51, 51, 52, 55, 56, 59, 70, 71,74, 76, 78, 84, 87,87, 90, 93 6. a. Obtain the five-number summary (i.e. Min, Q. Q: median, Qs, Max) for the data. Construct a box plot for the data For this frequency distribution, which measure of the center is larger, the median or the mean? (You do not have to calculate the mean to answer this question). c.

Answer 1

4)

a) Find the missing relative frequency

We know that, Total of relative frequency = 1

Therefore,

= 1 - (0.08 + 0.04 + 0.24 + 0.20 + 0.32)

= 1 - 0.88 = 0.12

Missing relative frequency is 0.12

b) How many student in the sample had a score of at least 63 ?

= 25 * (0.24 + 0.20 + 0.32)

= 25 * 0.76 = 19

19 student in the sample had a score of at least 63

C)

= 800 * (0.12 + 0.24 + 0.20)

= 800 * 0.56

= 448

448 student who scored 52-84 on the test