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The students in Marly's math class recorded the dimensions of their bedrooms in a frequency table.

Bedroom Areas

\begin{tabular}{|c|c|}
\hline
\begin{tabular}{c}
Area \\
(sq. ft)
\end{tabular} & \begin{tabular}{c}
Number of \\
Bedrooms
\end{tabular} \\
\hline [tex]$60 \leq A\ \textless \ 80$[/tex] & 4 \\
\hline [tex]$80 \leq A\ \textless \ 100$[/tex] & 6 \\
\hline [tex]$100 \leq A\ \textless \ 120$[/tex] & 5 \\
\hline [tex]$120 \leq A\ \textless \ 140$[/tex] & 3 \\
\hline [tex]$140 \leq A\ \textless \ 160$[/tex] & 1 \\
\hline
\end{tabular}

Create a histogram to represent the data.

Which statement is most likely true about the mean and the median of the data?

A. The histogram is right-skewed, so the mean is less than the median.
B. The histogram is right-skewed, so the mean is greater than the median.
C. The histogram is left-skewed, so the mean is less than the median.
D. The histogram is left-skewed, so the mean is greater than the median.

Sagot :

GinnyAnsweridn
To create a histogram, we plot the given ranges of bedroom areas against their frequencies. Here's the step-by-step way to do this:

1. Extract the Data:
- [tex]\(60 \leq A<80\)[/tex]: 4 bedrooms
- [tex]\(80 \leq A<100\)[/tex]: 6 bedrooms
- [tex]\(100 \leq A<120\)[/tex]: 5 bedrooms
- [tex]\(120 \leq A<140\)[/tex]: 3 bedrooms
- [tex]\(140 \leq A<160\)[/tex]: 1 bedroom

2. Draw the Histogram:
- On the x-axis, we have the ranges of the bedroom areas.
- On the y-axis, we have the number of bedrooms (frequencies).

3. Plot the Bars:
- For [tex]\(60 \leq A<80\)[/tex], draw a bar up to 4.
- For [tex]\(80 \leq A<100\)[/tex], draw a bar up to 6.
- For [tex]\(100 \leq A<120\)[/tex], draw a bar up to 5.
- For [tex]\(120 \leq A<140\)[/tex], draw a bar up to 3.
- For [tex]\(140 \leq A<160\)[/tex], draw a bar up to 1.

After drawing the histogram:

- The histogram shows the majority of the data is concentrated on the lower end of the scale, with a long tail to the right, indicating fewer larger bedroom areas.
- This type of distribution, with the tail extending to the right, is a right-skewed distribution.

Skewness and Measures of Central Tendency:
- In a right-skewed distribution, the mean is typically greater than the median. This is because the mean is influenced by the higher values in the tail, pulling it to the right of the median.

Conclusion:
The most likely true statement about the mean and the median of this data is:

The histogram is right-skewed, so the mean is greater than the median.
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