Question

A car salesperson sells cars at prices ranging from $5,000 to $45,000. The histogram shows the distribution of the numbers of cars he expects to sell over the next 10 years.

Answer 1

The median is the middle of the data.
Since the data is symmetric, the mean and median would both be the center of the distribution which is $25,000.
The data is is symmetric.

Answer 2

The median car price is $25,000. The distribution exhibits symmetry.

Explanation:

From the given histogram we get

Interval Frequency

5000-10000 200

10000-15000 350

15000-20000 550

20000-25000 700

25000-30000 700

30000-35000 550

35000-40000 350

40000-45000 200

From the table and graph, we conclude that the data is symmetric.

In a symmetrical data mean, median, mode and axis of symmetry are equal.

`\text{Axis of symmetry}=Mean=Median=Mode`

From the given graph it is clear that the graph is symmetrical about x=25000.

`Median=25000`

Therefore the median car price is $25,000. The distribution exhibits symmetry.