Question

1. given the histogram below, answer the questions: a) how would you describe the shape of this distribution? b) what would you estimate the mean and median to be? c) how many cars get between 25 - 30 mpg? d) what percent of cars get 15 - 20 mpg?

Explanation:

Step1: Calculate total number of people for first histogram

Sum up the frequencies in the age - based histogram.
\[10 + 50+20 + 15+20+15+10 = 140\]

Step2: Estimate median for first histogram

There are \(n = 140\) data points. The median is the average of the \(\frac{n}{2}=70\)th and \((\frac{n}{2}+ 1)=71\)st ordered data points. The first class (0 - 5) has 10, the second (5 - 10) has 50, so the median lies in the third class (10 - 15). A rough estimate could be around 12.

Step3: Analyze shape of second histogram

The second histogram is symmetric as the left - hand side is approximately a mirror image of the right - hand side.

Step4: Estimate mean and median for second histogram

For a symmetric distribution, the mean and median are approximately equal. The middle of the distribution seems to be around 17.5.

Step5: Find number of cars for second histogram (25 - 30 mpg)

From the second histogram, the frequency for the 25 - 30 mpg class is 15.

Step6: Calculate percentage for second histogram (15 - 20 mpg)

The total number of cars is \(15+20 + 35+25+15=110\). The number of cars in the 15 - 20 mpg class is 35. The percentage is \(\frac{35}{110}\times100\approx31.82\%\)

Answer:

a) 140
b) Approximately 12
c) Answers may vary, but could be a family - friendly movie given the age distribution.
a) Symmetrical
b) Approximately 17.5 for both mean and median
c) 15
d) Approximately 31.82%