Question

the following four sets of 7 numbers all have a mean of 9. complete parts (a) through (d) below. {9,9,9,9,9,9,9} , {8,8,9,9,9,10,10} , {6,6,6,9,12,12,12} , {4,4,4,9,14,14,14} make a histogram for set {4,4,4,9,14,14,14}. choose the correct answer below. a. b. c. d. (histogram options as described in the image)

Explanation:

Step1: Analyze the data set

The data set is \(\{4,4,4,9,14,14,14\}\). We count the frequency of each value: \(4\) appears \(3\) times, \(9\) appears \(1\) time, and \(14\) appears \(3\) times.

Step2: Match with histograms

We look for a histogram where the data values (x - axis) are \(4\), \(9\), \(14\) (or in bins around these values) and the frequencies (y - axis) are \(3\) for \(4\), \(1\) for \(9\), and \(3\) for \(14\). Looking at the options, option D has three bars: one at around \(4\) (frequency \(3\)), one at around \(9\) (frequency \(1\)), and one at around \(14\) (frequency \(3\)), which matches our frequency count.

Answer:

D. The histogram with data values on the x - axis (0, 3, 6, 9, 12), frequency on the y - axis (0, 1, 2, 3, 4), and bars: height 3 at around 4, height 1 at around 9, height 3 at around 14.