Question

which statement about the data is true?
the mean is greater than the median.
the mean is equal to the median.
the mean is less than the median.
done
of male dogs (lb.)
4 | 5
5 | 0, 2, 8
6 | 2, 8
7 | 2, 8
8 | 1
9 | 5
6|1 means 61?

Explanation:

To solve this, we first need to determine the data values from the stem - and - leaf plot. The stem - and - leaf plot has stems (the left - hand column) and leaves (the right - hand column).

Step 1: Extract the data values

• For stem 4: Leaf is 5, so the data value is 45.
• For stem 5: Leaves are 0, 2, 8, so the data values are 50, 52, 58.
• For stem 6: Leaves are 2, 8, so the data values are 62, 68.
• For stem 7: Leaves are 2, 8, so the data values are 72, 78.
• For stem 8: Leaf is 1, so the data value is 81.
• For stem 9: Leaf is 5, so the data value is 95.

Now, let's list out all the data values: 45, 50, 52, 58, 62, 68, 72, 78, 81, 95.

Step 2: Calculate the median

The median is the middle value of a sorted data set. Since we have \(n = 10\) (an even number of data points), the median is the average of the \(\frac{n}{2}\)-th and \((\frac{n}{2}+1)\)-th values.

\(\frac{n}{2}=\frac{10}{2}=5\) and \(\frac{n}{2}+1 = 6\).

The 5th value is 62 and the 6th value is 68.

Median \(=\frac{62 + 68}{2}=\frac{130}{2}=65\).

Step 3: Calculate the mean

The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(x_{i}\) are the data points and \(n\) is the number of data points.

\(\sum_{i = 1}^{10}x_{i}=45 + 50+52 + 58+62+68+72+78+81+95\)

\(45+50 = 95\); \(95+52 = 147\); \(147+58 = 205\); \(205+62 = 267\); \(267+68 = 335\); \(335+72 = 407\); \(407+78 = 485\); \(485+81 = 566\); \(566+95 = 661\)

Mean \(\bar{x}=\frac{661}{10}=66.1\)

Step 4: Compare the mean and the median

We have mean \(= 66.1\) and median \(= 65\). Since \(66.1>65\), the mean is greater than the median.

Answer:

The mean is greater than the median.