Teaching year is recorded as an integer, with first-year teachers recorded as 1, second-year teachers recorded as 2, and so on. Both sets of data have a mean teaching year of 8. 2, with data recorded from 200 teachers at High School A and 221 teachers at High School B. On the histograms, each interval represents possible integer values from the left endpoint up to but not including the right endpoint. (a) The median teaching year for one high school is 6, and the median teaching year for the other high school is 7. Identify which high school has each median and justify your answer. (b) An additional 18 teachers were not included with the data recorded from the 200 teachers at High School A. The mean teaching year of the 18 teachers is 2. 5. What is the mean teaching year for all 218 teachers at High School A

Respuesta :

The mean teaching year for all 218 teachers at High School A is 7.73 if the teaching year is recorded as an integer, with first-year teachers recorded as 1, second-year teachers recorded as 2, and so on.

What is a histogram?

It is defined as the numerical data representation in the graph with the help of a bar without space. The histogram gives an idea about the data's approximate distribution.

We have two histograms representing the teaching year with frequency.

From the first histogram the two reactangles represents = 45+48 = 93

From the second hisogram = 79+34 = 113

Median divided into two equal parts.

From the data:

The first graph has 200 points

The second graph has 221 points

The first graph median should be near the 100th data point

The second graph median should be the 111th data point

We obtain 93 from rectangles on a, which is less than 100, and these two rectangles include 1-4 and 4-7 (not including?) As a result, we might argue that this data covers 1-6.

We clearly need more values after we reach the medians, thus we must include the following interval. As a result, in a medium, 7 should be used.

The same reasoning applies to b), where the first two rectangles yield 113 and the median is the 111th datum point. We don't need to add these two rectangles because it includes them. So, for this median, the next interval (7-10) must be 6.

For part (b):

Mean of 18 = 2.5

= 2.5×18 ⇒ 45

Mean of 200 = 8.2

= 200×8.2 ⇒ 1640

New mean = Total/number of observation

= (45+1640)/(200+18)

= 1685/218

= 7.729

= 7.73

Thus, the mean teaching year for all 218 teachers at High School A is 7.73 if the teaching year is recorded as an integer, with first-year teachers recorded as 1, second-year teachers recorded as 2, and so on.

Learn more about the histogram here:

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