Question

describing a histogram
the histogram shows the average gas price by state in the us on december 4, 2018.
use the histogram to complete the sentences.
the shape of the histogram is
unimodal.
there an outlier.
the median average gas price is between $ and $
the varies from $2.00 to $3.75.

Explanation:

• Unimodal Shape: A unimodal histogram has one distinct peak. Looking at the histogram, we can observe that there is one main "bump" or peak in the data distribution, which is in the \(2.00 - 2.25\) price range.
• No Outlier: An outlier would be a data point that is far - removed from the rest of the data. In this histogram, all the bars (representing the number of states in each price interval) are relatively close in terms of their position on the price axis. There is no bar that is extremely separated from the others on the far left or far right.
• Median Calculation: The total number of states \(n\). Let's assume we count the frequencies: \(17+14 + 8+8+5+2+4=58\) (assuming the frequencies for intervals \(2.00 - 2.25\), \(2.25 - 2.50\), \(2.50 - 2.75\), \(2.75 - 3.00\), \(3.00 - 3.25\), \(3.25 - 3.50\), \(3.50 - 3.75\) respectively). Since \(n = 58\) (even), the median is the average of the \(\frac{n}{2}=29^{th}\) and \((\frac{n}{2}+1)=30^{th}\) ordered data points. Cumulative frequencies: \(17\) (up to \(2.25\)), \(17 + 14=31\) (up to \(2.50\)). So the \(29^{th}\) and \(30^{th}\) data points fall in the \(2.25 - 2.50\) interval.
• Data Range: The \(x\) - axis (price axis) of the histogram shows that the gas prices start at \(2.00\) and end at \(3.75\). The range of a data set (in the context of a histogram's \(x\) - axis for continuous data represented in intervals) is given by the minimum and maximum values of the variable. Here, the minimum value of the gas price variable (lower - bound of the first interval) is \(2.00\) and the maximum value (upper - bound of the last interval) is \(3.75\).

Answer:

• The shape of the histogram is unimodal.
• There is no an outlier.
• The median average gas price is between \(\$2.25\) and \(\$2.50\).
• The range varies from \(\$2.00\) to \(\$3.75\).