Question

question
based on the two data sets represented below, complete the following
sentences.
data set x
data set y
answer attempt 1 out of 2
the mean of data set x is than the mean of data set y. the
median of data set x is than the median of data set y.

Explanation:

Step1: Count the number of data points

For Data Set X:

• \(91:3\)
• \(92:3\)
• \(93:1\)
• \(94:3\)
• \(95:2\)
• \(96:3\)
• \(97:4\)
• \(98:3\)
• \(99:3\)

Total \(=3 + 3+1 + 3+2 + 3+4 + 3+3=25\)

For Data Set Y:

• \(89:5\)
• \(90:2\)
• \(91:3\)
• \(92:5\)
• \(93:3\)
• \(94:2\)
• \(95:2\)
• \(96:3\)

Total \(=5 + 2+3 + 5+3 + 2+2 + 3=25\)

Step2: Calculate the mean

For Data Set X:

$$
LATEXBLOCK0
$$

For Data Set Y:

$$
LATEXBLOCK1
$$

So mean of X \(>\) mean of Y

Step3: Calculate the median

Since \(n = 25\) (odd), median is the \(\frac{n + 1}{2}=13^{th}\) term.

For Data Set X:
Ordering (cumulative counts):

• Up to \(91:3\)
• Up to \(92:6\)
• Up to \(93:7\)
• Up to \(94:10\)
• Up to \(95:12\)
• Up to \(96:15\)

So \(13^{th}\) term is \(96\)

For Data Set Y:
Ordering (cumulative counts):

• Up to \(89:5\)
• Up to \(90:7\)
• Up to \(91:10\)
• Up to \(92:15\)

So \(13^{th}\) term is \(92\)

So median of X \(>\) median of Y

Answer:

The mean of Data Set X is greater than the mean of Data Set Y. The median of Data Set X is greater than the median of Data Set Y.