Question

4.7 a large high school has 149 teachers. the box - plot shows the distribution of the number of years of experience.

the histogram shows the distribution of the percent of the population that is urban for each of 216 countries/territories.

1. a is it possible to calculate the median urban population percent from the information given in the graph? explain.

b what interval contains the first quartile of the urban population percent?

1. a find and interpret the median number of years teaching experience.

b what percent of the teachers have 7 or more years of teaching experience?

c about how many of the teachers have between 7 and 23 years of experience?

Explanation:

Step1: Identify median from box - plot

The median is the middle - value in a data set. In a box - plot, the line inside the box represents the median. For the teachers' experience box - plot, the median is 11 years. This means that 50% of the 149 teachers have less than or equal to 11 years of teaching experience and 50% have more than 11 years of teaching experience.

Step2: Find percentage of teachers with 7 or more years of experience

The first quartile ($Q_1$) is at 7 years. Since 25% of the data is below $Q_1$, the percentage of teachers with 7 or more years of experience is $100 - 25=75\%$.

Step3: Estimate number of teachers between 7 and 23 years

The first quartile ($Q_1$) is 7 years and the third quartile ($Q_3$) is 23 years. The inter - quartile range (IQR) contains about 50% of the data. There are 149 teachers. So the number of teachers with between 7 and 23 years of experience is approximately $0.5\times149 = 74.5\approx75$.

Step4: Analyze median calculation from histogram

For the urban population histogram, we are given frequency intervals but not the exact data values within each interval. To find the median, we need to know the cumulative frequencies and the exact position of the middle value. Since we don't have the exact data points, it is not possible to calculate the median urban population percent from the information given in the graph.

Step5: Determine first - quartile interval

The total number of countries/territories is $n = 216$. The first quartile position is $Q_1=\frac{n + 1}{4}=\frac{216+1}{4}=54.25$. We calculate the cumulative frequencies for each interval. By looking at the cumulative frequencies, we find the interval that contains the 54.25th value.

Answer:

a. The median number of years of teaching experience is 11 years. This means 50% of the 149 teachers have less than or equal to 11 years of teaching experience.
b. 75% of the teachers have 7 or more years of teaching experience.
c. About 75 of the teachers have between 7 and 23 years of experience.
a. It is not possible to calculate the median urban population percent from the information given in the graph because we do not have the exact data values within each interval.
b. (Answer depends on cumulative - frequency calculation from the histogram, which is not shown in full here. But the general approach is to find the interval where the 54.25th value lies when arranging data in ascending order).