ONE-VARIABLE DATA: DISTRIBUTIONS AND MEASURES OF CENTER AND SPREAD 1 — Problem-Solving and Data Analysis

Questions in this quiz (7)

1. The frequency table below shows the number of hours spent studying per week by each of the $$48$$ students in a study group.A new student, who studies $$20$$ hours per week, joins the group. How do the mean and median of the number of hours studied by the new group of students compare to the mean and median of the original group?

   • The mean will increase, and the median will remain the same.
   • The mean will decrease, and the median will remain the same.
   • The mean will remain the same, and the median will increase.
   • Both the mean and the median will increase.

2. A data set consists of four numbers: $$5$$, $$8$$, $$12$$, and $$20$$. A fifth integer, $$w$$, where $$w$$ > $$0$$, is added to this set. If the mean of the new five-number data set is equal to its median, what is the value of $$w$$?

   • $$9$$
   • $$15$$
   • $$25$$
   • $$40$$

3. Two data sets, $$M$$ and $$N$$, are created from the information in the frequency table below. For each data set, each value is within the given range, inclusive, for the corresponding frequency.What is the greatest possible difference between the mean of data set $$M$$ and the mean of data set $$N$$?

   • $$\frac{1}{6}$$
   • $$\frac{5}{2}$$
   • $$\frac{38}{15}$$
   • $$\frac{15}{2}$$

4. Two data sets of $$20$$ integers each are summarized in the histograms shown. For each histogram, the first interval represents integers greater than or equal to $$10$$ but less than $$20$$, the second interval represents integers from $$20$$ up to $$30$$, and so on. What is the smallest possible difference between the mean of Data Set $$A$$ and the mean of Data Set $$B$$?

   • $$2.5$$
   • $$3$$
   • $$3.5$$
   • $$4$$

5. The number of packages a delivery driver delivered per day over $$5$$ consecutive days were $$14$$, $$18$$, $$21$$, $$26$$, and $$31$$. The mean number of packages delivered over these $$5$$ days was $$22$$. On the sixth day, the driver delivered $$11$$ packages. What is the median number of packages delivered over the $$6$$ days?

   • $$18$$
   • $$19.5$$
   • $$21$$
   • $$22.5$$

6. Group $$A$$ consists of the number of hours studied by $$50$$ students and has a mean of $$18$$ hours. Group $$B$$ consists of the number of hours studied by $$30$$ students and has a mean of $$28$$ hours. Group $$C$$ consists of the combined data from all students in Groups $$A$$ and $$B$$. What is the mean, in hours, of Group $$C$$?

   • $$20.25$$
   • $$21.75$$
   • $$22.50$$
   • $$22.75$$

7. A data set of $$21$$ different numbers has a mean of $$60$$ and a median of $$60$$. A new data set is formed by adding $$4$$ to each number in the original data set that is greater than the median and subtracting $$4$$ from each number that is less than the median. Which of the following measures does NOT have the same value in both the original and the new data sets?

   • Median and Mean
   • Mean and Range
   • Standard deviation only
   • Standard deviation and Range