### 7 April (Task 2b) Chap 16: Mean, Median & Mode - Let's see if I Understand...

This is a summary of the 3 types of Averages:
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Measures of Central Tendency or Averages

Arithmetic Mean
• The arithmetic mean of a set of numbers is the sum of numbers divided by the number of numbers in the set : Mean = sum of the numbers/number of numbers
• It is most the reliable measure provided there are no extreme values in the data because all the values in the data are used in calculating.
• Whenever the set of data contains extreme values, the median or mode would probably be more reliable because they are not influenced by extreme values.
Mode
• The number which occurs most frequently in a set of numbers
• It is most useful in business planning as a measure of popularity that reflects central tendency or opinion.
Median
• May be preferred as a measure of central tendency for describing economic, sociological and educational data.
• The median is popular in the study of social sciences because much of the data in the social sciences contain extreme values, in the set of household incomes.
• Median for an odd number of numbers is the middle number when the numbers are arranged in order of magnitude (i.e. ascending/descending order)
• Median for an even number of numbers is the mean of the two middle numbers when the numbers are arranged in order of magnitude
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Let's use the 3 types of averages to describe the set of data about the use of learning device after class.

1. Mean
(a) Describe how you would find the mean number of hours spend with the learning device after class.
(b) Compute the mean

2. Mode
(a) Describe how do you determine the mode of the data.
(b) What is the median number of hours?

3. Median
(a) Describe what must you do with the data before you can find the median.
(b) What is the median number of hours?

Remember to sign off with your name.

1. 1. Mean
(a) I would add all the hours together and divide them by the total number of pupils which is 23.
(b) The mean is 5 hours 34 minutes and 5.45 seconds.

2. Mode
(a) I would find the same of hours a pupil use his/her learning device each day.
(b) The median number of hours is 6.

3. Median
(a) Rearrange the numbers from the smallest and to the biggest and find the middle number.
(b) The median number of hours is 5.5

2. 1. (a) Add up all the numbers and divide them by 22.
(b) 5.57 hours

2. (a) Find the number that most frequently appear .
(b) The mode is 6.

3. (a) I must arrange the numbers in the ascending order before I can find the median.
(b) The median is 5.5 hours

Qian hui

3. 1. Mean
(a) I would total the number of hours and divide the answer by 22.
(b) 8+4+2+6+10+5+6+7+8+5+4.5+7+5+2.5+7+3+6+10+2+6+4.5+4=122.5
122.5÷22=5.7(approximated)

2. Mode
(a) I would tally the frequency of the respective hours and find the one with the highest frequency.
(b) 6 (The question asked for the median number of hours, but this question was the same as 3(b), so I found the mode instead)

3. Median
(a) We must rearrange the numbers in ascending/descending order, then find the median.
(b) 5.5 hours

4. 1. Mean
(a) Describe how you would find the mean number of hours spend with the learning device after class.
I would add all the hours up then divide it by 22.
(b) Compute the mean
It is about 5.6h (correct to 1 decimal place)

2. Mode
(a) Describe how do you determine the mode of the data.
I would see which number appears the most frequent.
(b) What is the median number of hours?
It is 6h.

3. Median
(a) Describe what must you do with the data before you can find the median.
I must arrange it in ascending order first.
(b) What is the median number of hours?
It it 5.5h.

5. 1.
(a)I would find the mean by adding all the hours together then dividing the sum by 22 as there are 22 students all together.

(b)5 25/44

2.
(a)I would put the data in ascending order then see which number appear the most then determine my mode.

(b)Is there a problem with this question since it is asking for mode instead of median???

3.
(a)We must first put the numbers in ascending order before we can find the median.

(b)5.5

6. Chan Shawn Kit4/07/2011 08:48:00 AM

1.A) Mean= Average of the sum of all the numbers.
Thus: X=sum of all numbers
X/22= Mean number of hours students spent on LD.
B)X=122.5h
122.5h/22=5.57h (3 significant figures)

2.A) Mode= Number that appeared the most in the data.
B) Mode of data=6h

3.A) All the numbers must first be arranged in ascending order. Then, as the total number of students is 22, the numbers 11 and 12 in order which is 5h and 6h is added together and divided by half which will be the median number.
B) Median of no. of hours spent on LD= 5.5h

7. 1. Mean
(a). I would add all the no. of hours and divide them by 22.
(b). 5Hours34mins5.45secs

2.Mode
(a). I would find the no. that most frequently appear in the data.
(b). 6

3.Median
(a).I would arrange the numbers in an ascending order and choose the number in the middle.
(b). 5.5 hours

Kai En~

8. This comment has been removed by the author.

9. 1. Mean
(a) I would add up the total hours of the pupils and divide it by 22 since there were 22 of them.
(b)5 hours 34mins 5.45 seconds

2.Mode
(a)I would find the most frequently appeared number.
(b)6

3.Median
(a) I would arrange them in ascending order and find the middle number, or the two numbers in the middle.
(b)5.5 hours.

Matthew Yap

10. 1.a) I would add together all of the figures and divide it by the number of numbers in the data.
b)Total hours= 122.5
122.5/22(Matthew was not present)The mean is (rounded off to first decimal place) 5.6 hours.

2.a) I would arrange all the numbers in ascending order and see what is the number that appears the most.
b)The mode is 6 and 7.
3.a)I would arrange the data in ascending order and take the total number of students( which is an even number) and divide by 2. After that I would count to the number from the start at the 11th number i would take that number and the next number. With those 2 numbers I would add them together and then divide them to get the median.
Or I could also add 1 to 22 and divide it by 2.
b)The median is 5.

11. 1.Mean
a) I will add all the number of hours and divide them by the total number of students.
b) 8+4+2+6+....+3+6+10+2+6 = 122.5
122.5 ÷ 22 ≈ 5.56
5.56hrs ≈ 5hrs and 34 mins
The mean is 5hrs and 34 mins.

2. Mode
a) I will find out which number in the table appear the most amount of times and that number will be the mode.
b) The median number of hours means which hour is at the middle of all the numbers in the table.

3. Median
a) I must re-arrange all the numbers in a accending order.
b) 5+6 = 11
11÷ 2 = 5.5
The median is 5.5hrs.

12. This comment has been removed by the author.

13. Its 22 not 23. (:

14. 1(a). Add all the time together. (Find the total) Divide the total by the number of the timings which is 22 and you will get the mean (average).

1(b). Total= 8+4+2+......6 No of nos=22
= 122 h and 30min

Mean(Average)= Total/No of nos
= 122h and 30min/22
= 5h,34min and 5.45 sec
Estimated to 5h and 34min. Ans:5h and 34min

2(a). Find the "most times of the number appearance", that number is the mode.
Eg. 1,1,2,3,4,5,5,5. 5 appear the most times so 5-->mode.

2(b) 6 appeared 4 times->most times. So, 6-->mode.

Ans:6

3(a) You have to arrange the numbers from ascending order.
Eg---> 1,6,5,4,8,9,7,3---> 1,2,3,4,5,6,7,8,9

3(b) The median is --> 2,2,3,4......5,6,.....10,10. 11th and 12th number is 6 so the median is (5+6)/2 = 5.5
Ans:5.5h

-Owen Ong Chau Siong(18)

15. This comment has been removed by the author.

16. 1a) I would calculate all the 22 number of hours together and then divide them by 22.
1b)8+4+2+6+10+5+6+7+8+5+4.5+4.5+7+5+2.5+7+4+3+6+10+2+6=245/44
60 x 245/44=334.09(repeat)
Mean Time=5h 34min 5.45sec

2a) I will count how many times each number repeats and then find which number repeats the most times.
2b) 2h= 2
2.5h=1
3h=1
4h=2
4.5h=2
5h=3
6h=4
7h=3
8h=2
10h=2
6 repeats the most times, so it is the modal number.
3a) I must arrange the numbers in ascending or descending order before calculating.
3b) 2,2,2.5,3,4,4,4.5,4.5,5,5,5,6,6,6,6,7,7,7,8,8,8,10,10
5+6/2=5.5
Median number= 5.5

Lam Jiajun

17. 1.
(a) I will add up all the numbers and divide it by the number of numbers
(b)5 hours,34min and 5.45 seconds

2.
(a)I would arrange all the numbers in a line from smallest to biggest and see which number appears most amount of times
(b)6

3.
(a)I must arrange all the numbers from smallest to biggest before i can find the median,then i will find the number that is in the middle of the number line,if there is a even number of numbers i would take the two numbers and find the average
b)5.5

18. 1 a) I would add all the number hours together and divide it by 22 pupils who were present at the scene.
b) approximately 5.57 hours.

2a)I will arrange the numbers in ascending order and find out the number that appear most frequent.
b)The mode is 6.

3 a) I will arrange the numbers in ascending order and I can find out the median number easily.
b) The median number is 6.

19. 1. Mean
(a) Describe how you would find the mean number of hours spend with the learning device after class.
Add all the hours together and divide by 22.
(b) Compute the mean
5.56hrs (3SF)

2. Mode
(a) Describe how do you determine the mode of the data.
Find out which number of hours has the highest frequency.
(b) What is the mode of the number of hours?
6 hrs

3. Median
(a) Describe what must you do with the data before you can find the median.
Arrange them in Ascending order first.
(b) What is the median number of hours?
5.5hrs

20. Mark :) :( :&#39;( (^^^) :D :O :42: O:) :p 3:)4/07/2011 09:49:00 AM

1. Mean
a) I would add all the number of hours and divide them by 22 to find the mean number of hours
b)5 hours 34 minutes and 5.45 seconds

2. Mode
a) I would find the number that appears most frequently on the data.
b) 6

3. Median
a) I would arrange the numbers in line in ascending order and choose the number directly in the center, or if the number of data points are even, then i would pick the middle two numbers and find the mean of them.
b) 5.5 hours

21. 1. Mean
(a) Add the number of hours and divide it by 22.
(b) 5.6 hours(correct to 1 decimal place)
2. Mode
(a) The number that appears most in the data is the mode.
(b) 6 hours
3. Median
(a) Arrange the number of hours in ascending order and take the number that is in the middle when the number of numbers is odd. When the number of numbers is even, take the two numbers that are in the middle and divide them by two.
(b) What is the median number of hours?
5.5 hours

Ding Nina Lin

22. 1. Mean
(a)i added all the hours and divided it by the number of students in the class(8+4+2+6+10+5+6+7+8+5+4.5+7+5+2.5+7+3+6+10+2+6+4.5+4/22=122.5/22)
(b) 5.57(3 significant figures)
2. Mode
(a) I would see which number appeared most frequently.
(b) 6
3. Median
(a) I would arrange the numbers in order of magnitude.Take the total number of students in the class, divde it by 2(11), and add 1(12).Therefore the position would be 11+12/2=11.5.
(b) The number between the 11th position(5)and 12th position(6) is 5.5hours
Liew Wei Siew

23. 1. Mean

(a) Describe how you would find the mean numbers of hours spend with the learning device after class.

I would add all the numbers of the given data to find out the sum of all the numbers and count the number of values in the given data . Using the two calculated values , divide the sum of all the numbers by the number of values .
(b) Compute the mean

5.6 ( 1 decimal place)

2. Mode
(a) Describe how do you determine the mode of the data.

Arrange the numbers in the given data in ascending order and find our the number that has the most frequency .

(b) What is the mode number of hours?

6 hours

3. Median
(a) Describe what must you do with the data before you can find the median.

I would arrange the numbers in ascending order. I will pair the number on the right and the number on the left . This will continue until the pairing reaches the last pair as there are a even number of values. Add the pair of numbers together and divide it by two .

(b) What is the median number of hours?

The last pair - 5 and 6
5+6 = 11
11/2 = 5.5 hours

Cheng Shu Yu Mavis(1) S1-01

24. 1. Mean
[a] I will add all the hours together and divide the sum by the number of hours.
[b] 8+4+2+6+10+5+6+7+8+5+4.5+4.5+7+5+2.5+7+4+3+6+10+2+6 / 22 ≈ 5.57(3 S.F.)

2. Mode
[a] Find out which is the number that appears the most.
[b] 6 hours

3. Median
[a] Arrange the numbers in ascending order.
[b] 2, 2, 3, 4, 4, 4.5, 4.5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 10
5+6 / 2=5.5

25. 1. Mean
(a) I would total the number of hours and divide the answer by 22.
(b) 8+4+2+6+10+5+6+7+8+5+4.5+7+5+2.5+7+3+6+10+2+6+4.5+4=122.5
122.5÷22=5.57(3sf)

2. Mode
(a) I would see which number appears the most.
(b) 6

3. Median
(a) We must rearrange the numbers in ascending/descending order, then find the middle of the numbers.
(b) 2, 2, 3, 4, 4, 4.5, 4.5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 10
5+6 / 2=5.5 hours

26. 1.Mean
(a)I would add the numbers of hours and divide the answer by 22
(b)5.6
2.Mode
(a)I would see which number appears the most.
(b)6
3.Median
(a) I would arrange the number in ascending order then find the middle number.
(b) 5.5hours