Question

If there is a large amount of raw data, a split stem and leaf may be used. In a split stem and leaf plot graph, the stem is listed twice. Leaves 0 through 4 are listed on the first row and leaves 5-9 are listed on the second row. The following is a split stem and leaf plot. Ages of People at a Reunion 0 123 334 079 14 1 5 5 5 6 6 2 3 34 2 557 888 0112 566 4 119 5 0 1 2 5 89 Key: 215= 25 years old Using the data in the split stem and leaf plot answer the following questions. How many raw data values are in the data set: N- The smallest raw data value is and the largest raw data value is What is the mode? What is the mean? (Round to the nearest tenth.) What is the median?

Answer 1

The split stem and leaf plot includes 21 data points, with the smallest age being 23 and the largest 56. The mode of the dataset is 55, and the mean age, rounded to the nearest tenth, is 39.6. The median is 39.

Step-by-step explanation:

The student provided a split stem and leaf plot representing the ages of people at a reunion. To analyze the data, we must first comprehend the format of the stem and leaf plot and how to interpret it. The plot has stems that are split into two rows for each value, one for leaves 0 through 4 and one for leaves 5 through 9. To determine N, the total number of data values, we simply count the leaves. The smallest and largest values are identified by looking at the extremes of the plot. By counting the most frequent leaves, we can determine the mode. To calculate the mean, we sum all the ages and divide by N, rounding the result to the nearest tenth. The median is the middle value when all the ages are ordered from smallest to largest.

Analysis:

• Raw data values (N): After counting, there are 21 ages in total.
• Smallest raw data value: The smallest age is 23.
• Largest raw data value: The largest age is 56.
• Mode: The most frequent age, occurring four times, is 55.
• Mean: The sum of all ages is 831. Divided by 21, the mean age is 39.6 when rounded to the nearest tenth.
• Median: The 11th value in the ordered list is 39, which is the median age.

Answer 2

Answer: To answer the questions, let's first organize the data in ascending order:

0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 8, 8, 8, 8, 9, 9, 9, 11, 12, 14, 19, 23, 25, 34, 34, 55, 56, 66, 79, 88, 88, 89, 119, 215, 566

Now, let's answer the questions:

How many raw data values are in the data set (N)?

Counting the number of data values, we find that there are 45 raw data values in the data set.

The smallest raw data value is:

The smallest raw data value in the data set is 0.

The largest raw data value is:

The largest raw data value in the data set is 566.

What is the mode?

The mode is the value that appears most frequently in the data set. In this case, the value "5" appears the most times (six times), so the mode is 5.

What is the mean?

To find the mean, sum all the data values and then divide by the total number of data values (N):

Mean = (0 + 0 + 1 + 1 + 2 + 2 + ... + 215 + 566) / 45

Mean ≈ 132.2 (rounded to the nearest tenth)

What is the median?

The median is the middle value when the data is arranged in ascending order. Since there are 45 data values, the median is the average of the 22nd and 23rd values:

Median = (5 + 5) / 2

Median = 5

So, the median is 5.