Question

36. The histogram shows the ages of the first 45 U.S. presidents on their firstInauguration Day.13TFrequency12111098765432104075Age (years)The ages of 20 of the 45 presidents are shown below.42, 43, 45, 46, 49, 52, 53, 54, 54, 57, 57, 58, 59, 61, 62, 62, 66, 66, 69, 72A certain president's age is in the interval labeled T.What could be the acceptable range for the interval?42 to 4443 to 4945 to 4947 to 54

Answer 1

Note that the graph shows us that the minimum and maximum value of the ages are 40 and 75, respectively.

We can count the number of bars on the histogram. We see that the are 7 bars in total.

Each bar consider the same age span, so that means that each bar represent an age span of the same amount of years.

To calculate this range, we first find the difference between the maximum and the minimum, that is

$75-40=35$

Now, we divide this number by the total number of bars. That is

$\frac{35}{7}=5$

So, each bar represents a range of 5 years .

Since the minimu is 40, this means that the first bar should represent ages from 40-44. Note that despite the difference between 44 and 40 is only 4, since we are including age 40 in the first bar, we have numbers 40,41,42,43,44 (5 numbers ) associated to the first bar.

This means that for the next one, which is the range T we are looking for, the correspondent age range should be 45-49