Question

2. A teacher asked his class of 20 students, "What is your age? Their responses are shown in the dot plot below.

Mean =
Median =
x
À Xxx
XXXXX
Mode =
Range =
14
15
17
18
16
Age
Does the mean or median best represent the center for this data? Explain.​

Answer 1

a) Mean = 16.09

Median = 16

Mode is highest frequency = 16

Range = highest number - lowest number

Range = 19 - 14 = 5

b) median

Explanation:

The mean = [(4×14) + (5×15) + (6×16) + (3×17) + (4×19)] ÷ 22

Mean = (56+75+96+51+76)/22

Mean = 354/22

Mean = 16.09

Median = 16

Mode is highest frequency = 16

Range = highest number - lowest number

Range = 19 - 14 = 5

Measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data.

The mean is most likely the measure of central tendency that is very popular with, but in this question, median best represent the center for this data because of its single value.

Answer 2

Yes, average does represent the centre of this data.

Average = 15.9

Explanation:

As this question is not complete and not correctly written. Let's try to find an answer for this question.

Total number of Students = 20 = n

and we are given this data:

14, 15, 17, 18, 16.

which is just five entries and total number of students are 20. 15 entries are missing in this questions. So, let's add our own values into this question.

New set of entries for 20 students.

1. 14

2. 15

3. 17

4. 18

5. 16

6. 19

7. 17

8. 16

9. 17

10. 17

11. 15

12. 20

13. 14

14. 17

15. 18

16. 19

17. 13

18. 20

19. 17

20. 16

So, let's calculate the average of these numbers.

Average = Sum of all entries/ Total number of entries.

Average = 318/20

Average = 15.9

So, the average age of all the students of class is 15.9.

Let's calculate median:

For median , data must be arranged in a order from least to greatest number. Median is a number from that data which is at half way. In case of odd numbers, it is easy to identify median because there is only one number. and in case of even numbers, median is the average of the two middle numbers. So, here we have even numbers and median is the average of two middle numbers = 17 + 17/2 = 17

Median = 17

Yes, average does represent the centre of this data.