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The data below show the approximate number of students at 10 schools in District A and District B who ride the bus daily.

District A: 300,400,410, 360, 270, 290, 460, 300, 340, 420
District B: 310, 240, 190, 290, 320, 390, 240, 210, 270, 240
which statement comparing the bus riders in each district is true?
A - the median number of bus riders is greater in district b than in district a
B - the mode of bus riders is greater in district b than in district a
C - the mean number of bus riders is greater in district a than in district b
D - the range of bus riders is greater in district a than in district b

1 Answer

4 votes

To compare the bus riders in each district, we can calculate the median, mode, mean, and range of each set of data:

For District A:

Median: To find the median, we need to arrange the numbers in order from least to greatest: 270, 290, 300, 300, 340, 360, 400, 410, 420, 460. The median is the middle number, which is 340.

Mode: The mode is the number that appears most frequently. In this case, there is no mode, since no number appears more than once.

Mean: The mean is the average of the numbers. We can add up all the numbers and divide by the total number of numbers: (300+400+410+360+270+290+460+300+340+420) / 10 = 350.

Range: The range is the difference between the largest and smallest numbers. In this case, the range is 460 - 270 = 190.

For District B:

Median: To find the median, we need to arrange the numbers in order from least to greatest: 190, 210, 240, 240, 240, 270, 290, 310, 320, 390. The median is the average of the middle two numbers, which are 250 and 270. The median is (250 + 270) / 2 = 260.

Mode: The mode is the number that appears most frequently. In this case, the mode is 240, since it appears three times.

Mean: The mean is the average of the numbers. We can add up all the numbers and divide by the total number of numbers: (310+240+190+290+320+390+240+210+270+240) / 10 = 267.

Range: The range is the difference between the largest and smallest numbers. In this case, the range is 390 - 190 = 200.

Based on these calculations, we can determine that:

A) The median number of bus riders is greater in district A than in district B, since the median for district A is 340 and the median for district B is 260.

B) The mode of bus riders is greater in district A than in district B, since district A has no mode, and district B has a mode of 240.

C) The mean number of bus riders is greater in district A than in district B, since the mean for district A is 350 and the mean for district B is 267.

D) The range of bus riders is greater in district A than in district B, since the range for district A is 190 and the range for district B is 200.

Therefore, statement C - the mean number of bus riders is greater in district A than in district B - is the true statement.

User Federico Builes
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