Question

enter two or more numbers in the table to create a histogram. enter the data to create a histogram. then select the correct answer. hours 3 4 4 2 5 4 6 6 5 faizah keeps track of the hours she practices. the histogram is not symmetrical. the histogram is symmetrical. the data are not evenly distributed. the left side of the graph is not the mirror image of the right side of the graph. show histogram.

Explanation:

First, we need to understand the concepts of symmetry in a histogram. A symmetrical histogram has a mirror - image relationship between the left and right sides.
For the data set \(2,3,4,4,4,5,5,6,6\), when we create a histogram (assuming appropriate binning, for example, bin \(2 - 2.99\), bin \(3 - 3.99\), bin \(4 - 4.99\), bin \(5 - 5.99\), bin \(6 - 6.99\)).
The frequencies for the bins: bin \(2 - 2.99\) has a frequency of \(1\), bin \(3 - 3.99\) has a frequency of \(1\), bin \(4 - 4.99\) has a frequency of \(3\), bin \(5 - 5.99\) has a frequency of \(2\), bin \(6 - 6.99\) has a frequency of \(2\).
If a histogram is symmetrical, the frequencies on the left - hand side of the center bin (when ordered) should be the same as the frequencies on the right - hand side. Here, the center of the ordered data (in terms of binning) is around the bin \(4 - 4.99\). The sum of frequencies of bins to the left of \(4 - 4.99\) (\(1 + 1=2\)) is equal to the sum of frequencies of bins to the right of \(4 - 4.99\) (\(2+2 = 4\)) which is not equal. Also, a symmetrical histogram implies even distribution in a sense of mirror - image.

Answer:

The histogram is symmetrical.