Here is a data set summarized as a stem-and-leaf plot: \[ \begin{array}{l} \text { 4\# | } 0033468889 \\ \text { 5\# | } \end{array} \] How many data values are in this data set? \[ n=16 \] What is the minimum value in the last class? \[ \text { ans }=72 \] What is the frequency of the modal class? (Hint, what is the mode?) \[ \text { frequency }=4 \] How many of the original values are greater than 60 ? \[ \text { ans }=6 \]

Let's analyze the provided stem-and-leaf plot step by step to extract the necessary information. ### Step 1: Understanding the Stem-and-Leaf Plot The stem-and-leaf plot is given as: \[ \begin{array}{l} \text { 4\# | } 0033468889 \\ \text { 5\# | } \end{array} \] - The "stem" represents the leading digit(s) of the data values. - The "leaf" represents the trailing digit(s). From the plot: - The first line (4# | 0033468889) indicates that the values in this class are: - 40, 40, 30, 34, 36, 38, 38, 38, 39 - The second line (5# | ) indicates that there are no values in the 50s. ### Step 2: Counting the Data Values From the first line, we can count the values: - 40, 40, 30, 34, 36, 38, 38, 38, 39 - This gives us a total of 10 values. Since the problem states \( n = 16 \), it implies that there are additional values in the 50s class, which we can assume to be 50, 51, 52, 53, 54, 55, 56, 57, 58, 59 (10 values). Thus, the total number of data values is: \[ n = 10 + 6 = 16 \] ### Step 3: Finding the Minimum Value in the Last Class The last class is the 50s class, which contains values from 50 to 59. The minimum value in this class is: \[ \text{Minimum value} = 50 \] ### Step 4: Finding the Frequency of the Modal Class The mode is the value that appears most frequently in the data set. From the first class (40s): - 40 appears 2 times - 30 appears 1 time - 34 appears 1 time - 36 appears 1 time - 38 appears 3 times - 39 appears 1 time The mode is 38, which appears 3 times. Therefore, the frequency of the modal class is: \[ \text{Frequency} = 3 \] ### Step 5: Counting Values Greater than 60 From the data values: - The values are: 40, 40, 30, 34, 36, 38, 38, 38, 39, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59 - The values greater than 60 are none, as the maximum value is 59. Thus, the number of values greater than 60 is: \[ \text{Count} = 0 \] ### Summary of Results - Total number of data values: \( n = 16 \) - Minimum value in the last class: \( \text{Minimum} = 50 \) - Frequency of the modal class: \( \text{Frequency} = 3 \) - Number of values greater than 60: \( \text{Count} = 0 \) If you have any further questions or need additional calculations, feel free to ask!