a neighborhood is trying to set up school carpools, but they need to determine the number of students that need to travel to the elementary school (ages 5–10), the middle school (ages 11–13), and the high school (ages 14–18). a histogram summarizes their findings:
histogram titled carpool, with number of children on the y axis and age groups on the x axis. bar 1 is 5 to 10 years old and has a value of 7. bar 2 is 11 to 13 years old and has a value of 5. bar 3 is 14 to 18 years old and has a value of 4.
which of the following data sets is represented in the histogram?
{15, 6, 7, 16, 11, 13, 8, 9, 12, 14, 14, 12, 11, 5, 10, 10}
{7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 4, 4, 4, 4}
{5, 7, 10, 5, 11, 13, 4, 14, 18}
{5, 6, 7, 8, 14, 18, 16, 17, 11, 12, 13}

The correct option is 1.

Step-by-step explanation:

From the given histogram it is clear that

In age group 5-10, the number of students is 7.

In age group 11-13, the number of students is 5.

In age group 14-18, the number of students is 4.

It means age of 7 students lie in the interval 5-10, age of 5 students lie in the interval 11-13 and age of 4 students lie in the interval 14-18.

Total number of elements in the data set is

In option 3 and 4 number of elements is data set is less than 16. So, option 3 and 4 are incorrect.

In option 2 all the data set lie in the interval 5-10. So, option 2 is incorrect.

In option 1,

Class intervals      elements           frequency

5-10                    5,6,7,8,9,10,10           7

11-13                  11,11,12,12,13            5

14-18                    14,14,15,16              4

From the above table we can conclude that data set 1 represented in the given histogram.

Therefore the correct option is 1.

The only correct option is a) {15, 6, 7, 16, 11, 13, 8, 9, 12, 14, 14, 12, 11, 5, 10, 10} because total number elements in option a) is equal to 16.

According to histogram,

Total number of elements = 7 + 5 + 4 = 16.

Now we can find answer by eleminating the options:

In option a):

Class intervals        elements           frequency

5-10                        5,6,7,8,9,10,10            7

11-13                        11,11,12,12,13                5

14-18                        14,14,15,16                  4

Option a) is correct because total number elements is equal to 16.

In option b) all the data set lie in the interval 5-10. So, option 2 is incorrect.

In option c) and d) number of elements is data set is less than 16. So, option c) and d) are incorrect.

Therefore, the only correct option is a) {15, 6, 7, 16, 11, 13, 8, 9, 12, 14, 14, 12, 11, 5, 10, 10}.

For more information, refer the link given below

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step-by-step explanation:

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