Homework

Mean, Mode and Median

1. Given that the mean of m, 9, 6 and n is 4 and the mean of 2/7, 17, m/n, 14 and 28 is 12, find the values of m and n.

2. The table below shows the number of hours a group of students spent on watching television in a day. Given that the total number of students was 42 and the average

number of hours was h, find the values of m and n.

No. of hours 2 3 4 5 6No. of students 10 m 12 8 n

3. p and q are 2 numbers in a set of 6 numbers with an average of 30. p is the bigger number and the difference between p and q is 6. The other 4 numbers are also in another set of 6 numbers with an average of 37⅔. The other 2 numbers in the second set of 6 numbers have an average of 38. Find the values of p and q.

4. The table below shows the travelling time of a group of students.

Time (min) 35 40 45 50No. of students 25 m + 2 m 8

Given that the median is 40, find the smallest possible value of m.

5. The table below shows the number of siblings a group of students have.

No. of siblings 0 1 2 3 4No. of students 5 p 12 6 2

Given that the median is 1, find the smallest possible value of p.

6. In a school, the number of students in the respective age groups are as follows:

Age (year) 7 8 9 10 11No. of students 5 7 10 4 x

Given that the median is 9, find the largest possible value of x.

7. A set of 5 fractions with a denominator of 4 has a mode of 9/4, a median of ¾ and a mean of 1.2. Find the 5 fractions.

8. The table below shows the marks of a group of students in a Geography test.

Marks 25 30 35 40No. of students 5 q 12 10

Given that the median is 35, find the largest possible value of q.

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9. A group of students were told to report their marks in a Mathematics test to their teacher. The following table shows their marks in the Mathematics test.

Marks 30 35 40 45No. of students 8 12 y 10

(a) Given that the average mark is 37.75, find y.(b) After the 39th student reported his mark to the teacher, the median mark is 35. What

are the possible marks obtained by the next student?

10. The mass of a class of 40 students are given in the table below.

Mass (kg) 30 32 34 36 38 40No. of students 9 8 m n 6 5

Given that the average mass is 34.25 kg, find the median.

11. The mean of 10, 13, 15, x, y and z is 23. The mean of 8, 10, 14, x and y is 18. If x and 2y are added to the original 6 numbers, the mean becomes 25. Find the values of x, y and z.

12. The table below shows the timing for a 2.4-km run for the some students.

Time (min) 13 14 15 16 17No. of students 7 9 12 5 n

(a) Given that the average time is 14.9 min, find n.(b) The teacher realised that he left out the records of 2 more students and added them in.

If the new mean is 15 min, find the timing of the 2 new students.

13. The scores of a group of students in a quiz are shown in the stem-and-leaf diagram below.

Stem Leaf

1 0 0 1 2 32 1 1 2 3 y 63 0 1 1 7 7 x4 8 8 z

Key: 1 | 0 means 10 marks

Given that the mode is 37, mean is 27.1 and median is 25.5, find the values of x, y and z.

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14. The incomplete histogram below shows the number of medals won by an athlete in 25 competitions.

Given that the mean is 2.2, complete the histogram above.

15. The stem-and-leaf diagram below shows the mass of a class of students.

Stem Leaf

3 5 5 6 7 8 84 2 2 2 2 x 5 55 0 8 y 9 9 96 z

Key: 3 | 5 means 35 kg

Given that the median is 42.5 kg, the mode is 42 kg and that if one more student whose mass is 63 kg joins the group, the difference in the mean is 0.8 kg, find the values of x, y and z.

16. The table below shows the number of latecomers in a school from January to May.

Month Jan Feb Mar Apr MayNo. of latecomers 10 12 9 15 20

If the number of latecomers for June and July are included, the new mean is 14. The ratio of the number of latecomers in June to the number of latecomers in July is 7 : 9. Find the number of latecomers in June and July respectively.

End of Homework

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