Introduction
Good morning learners. Today we are going to start a new topic called Data Handling, we are going to focus on Summarizing Data. Please watch the 3 minuter video ,where I introduce the concept. Stay safe and stay tuned!
Task
Please complete the following activity
Question 1
1.In a times table test, a group of 9 children scored 25, 17, 21, 25, 23, 21, 27,21 and 18 out of a total of 30. Find their mean, median, mode and range.
2.The salamanders have a competition to see how far they can jump. Find the mean, median, mode and range. Their results are as follows:
Captain Sally Quadra Tiger Frazer Quadra
2.3m 3.5m 1.7m 4.3m 2.1m 1.7m
3. On a day in January the temperature for 7 places around the world are as follow:
Amsterdam 5°C Hong Kong 15°C Moscow -17°C
Cape Town 20°C Minneapolis -21°C New York -6°C
Find the mean, median, mode and range
Question 2
1.In a spelling test, some children in a class scored 13, 17, 12, 19, 20, 13 and 11 out of a total of 20. Find their mean, median, mode and range.
2. Eleven runners are raising money for charity by running round a track. Here are the numbers of laps they manage to run. Number of laps: 15, 12, 8, 26, 14, 11, 8, 15, 9, 10 and 15. Find their mean, median, mode and range.
3.An ice-cream vans ells a range of different ice creams for 2 weeks. This is the number of ice-cream he manages to sell.
Week 1: 87, 75, 95, 102, 109, 61, 85 Week 2: 77, 103, 102, 79, 8, 63, 70
Find the mean, median, mode and the range of his ice-cream sales.
Process
Mean
To calculate the mean, you add all the values of the data set and divide this sum by the total
number of values in the data set.
𝑀𝑒𝑎𝑛 = 𝑠𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙 𝑣𝑎𝑙𝑢𝑒𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑑𝑎𝑡𝑎 𝑠𝑒𝑡 / 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑣𝑎𝑙𝑢𝑒𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑑𝑎𝑡𝑎 𝑠𝑒𝑡
Note: the mean can only be calculated if the data is numerical
Example:
The soccer team kept a record of the number of goals scored, as shown below, in all the matches they played in the recent season:
1 7 9 4 3 5 8 3 2 8
1. How many matches did the soccer team play?
2. Calculate the mean score.
3. How many matches produced a result above the mean score?
Solutions:
1. 10 matches as there are 10 scores
2. 𝑀𝑒𝑎𝑛 = 𝑠𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙 𝑣𝑎𝑙𝑢𝑒𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑑𝑎𝑡𝑎 𝑠𝑒𝑡 / 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑣𝑎𝑙𝑢𝑒𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑑𝑎𝑡𝑎 𝑠𝑒𝑡
𝑀𝑒𝑎𝑛 = 1 + 7 + 9 + 4 + 3 + 5 + 8 + 3 + 2 + 8
10
= 50 /10
= 5
3. 4 matches as there were 4 scores greater than 5 (i.e. 7; 9; 8 and 8)
Median
• The median is the middle value of a data set that is arranged in ascending (smallest to
biggest) order
• If there is an odd number of values in the data set, the middle value will be the median
• If there is an even number of the values in the data set, you will have two values in the middle.
In this case, you need to find the mean of these two middle values, i.e. add them together
and divide by 2
Example
1. Odd number of data values
The list below shows the first round scores obtained by golfers in a school tournament:
83 89 88 90 89 84 82 86 89 87 86
Determine the median:
• Firstly, arrange the data set in ascending order
82 83 84 86 86 87 88 89 89 89 90
The middle value is the median
Median = 87
2. Even number of data values
The soccer team kept a record of their match scores, as shown below:
1 7 9 4 3 5 8 3 2 8
Calculate the median score.
• Firstly, arrange the data set in ascending order
1 2 3 3 4 5 7 8 8 9
No middle value, therefore add 4 and 5 and divide by 2
4+5 = 9
9÷2 = 4,5
Median match score is 4,5 goals
Mode
• The mode is the value (or values) in the data set, that occur(s) most frequently
Example
The soccer team kept a record of their match scores, as shown below:
1 7 9 4 3 5 8 3 2 8
Calculate the modal score:
3 and 8 have the highest frequency – both appear twice
The data set is said to be bi-modal, i.e. the mode is 3 and 8
Measure of spread
Range
Range = highest value – lowest value
Example: 7, 5, 12, 45, 1
45 - 1 = 44
Range = 44
Evaluation
|
Section A |
|||
|
Question 1 |
Marks for Calculation (8) |
Marks for Answer (4) |
Total (12) |
|
Q.1 |
|
|
|
|
Q.2 |
|
|
|
|
Q.3 |
|
|
|
|
|
|||
|
Question 2 |
Marks for Calculation (8) |
Marks for Answer (4) |
Total (12) |
|
Q.1 |
|
|
|
|
Q.2 |
|
|
|
|
Q.3 |
|
|
|
|
|
|
|
|
|
Total |
|
/72 |
Conclusion
- Make sure you can summaries one set of data.
- Make sure you can identify the most appropriate measure of central tendency.
- Make sure that you revise and practice all the steps that was taken in order to calculate the MEAN, MEDIAN. MODE AND RANGE
Have a good day students!
Credits
Students I've added some sources that will help you revise on today's lesson. Please watch them it's going to benefit you for your next test!
Grade 10 Maths Lit Data Handling
Math Antics - Mean, Median and Mode
Teacher Page
Cady Hammerse
Student Number: 219025053