In this worksheets, students will identify Action and Linking verbs, this will help them to enhance their knowledge about the verbs: (Answers are also provided at the end of the worksheet)
Verbs- WS 2
In this worksheets, students will identify Action and Linking verbs, this will help them to enhance their knowledge about the verbs: (Answers are also provided at the end of the worksheet)
Verbs- WS 3
In this worksheet, students will identify the Action verbs, it will improve their understanding about the action verbs. (Answer keys are also provided at the end of the worksheet.)
Find Mean, Median, Mode & Range- WS3
A. Find the mean, median, mode and range of the following data sets:
1. 13, 18, 13, 14, 13, 16, 14, 21, 13
Mean: _____ Median: _____
Mode: _____ Range: _____
Find Mean, Median, Mode & Range- WS2
Name:_______________________________ Date:_____________________
1. Sara Lee earned scores of 98, 100, 65, 78, 98, 35, 100, 100, 45, and 50 on her reading tests. What is the mean of her test scores?
2. A family decides to hold two Christmas parties, one on Christmas Eve and one on Christmas Day. The youngest person to attend the Christmas Eve party is 15 and the oldest is 29. The youngest person to attend the Christmas Day party is 27 and the oldest is 42. Which party has a larger age range of visitors?
Find Mean, Median,Mode &Range- WS1
1. What do you understand by Mean, Median, Mode and Range of a data?
Statistics- Lesson 1
Mean: The average of numbers (data values) is called mean.
Rule to find the mean of a data set: Add all the numbers in a given data set and divide the sum with the number of data values in the set.
Example: Suppose we have to find the mean of the data set: 12, 22, 24, 27, and 35.
Step 1: add all numbers to find their sum:
Median: The middle value of a sorted data set is called the median of the set.
Rule to find the mean of a data set:
(1) If number of data values in a set is odd: suppose we need to find the median of data set 5, 7, 23, 21, 15, 30, 27
First, arrange all the values in ascending (smallest to greatest) order as,
5, 7, 15, 21, 23, 27, 30
Now, we have 7 data values (or simply we have 7 numbers in the set), find the middle number of the set, that will be the median of the set.
5, 7, 15, 21, 23, 27, 30
Here 21 is the middle number in the set, so the median of the set is 21
(2) If number of data values in a set is even: In this case, we will find the middle two terms and then the mean of middle two terms will be the median of the data set.
suppose we need to find the median of data set 5, 7, 23, 21, 15, 30, 17, 27
First, arrange all the values in ascending (smallest to greatest) order as,
Rule to find the mean of a data set: Add all the numbers in a given data set and divide the sum with the number of data values in the set.
Example: Suppose we have to find the mean of the data set: 12, 22, 24, 27, and 35.
Step 1: add all numbers to find their sum:
12 + 22 + 24 + 27 + 35 = 120
Step 2: Then we take this sum and divide it by the number of values in the set (which is 5):120 ÷ 5 = 24
The result 24, is the mean (average) of the data set.Median: The middle value of a sorted data set is called the median of the set.
Rule to find the mean of a data set:
(1) If number of data values in a set is odd: suppose we need to find the median of data set 5, 7, 23, 21, 15, 30, 27
First, arrange all the values in ascending (smallest to greatest) order as,
5, 7, 15, 21, 23, 27, 30
Now, we have 7 data values (or simply we have 7 numbers in the set), find the middle number of the set, that will be the median of the set.
5, 7, 15, 21, 23, 27, 30
Here 21 is the middle number in the set, so the median of the set is 21
(2) If number of data values in a set is even: In this case, we will find the middle two terms and then the mean of middle two terms will be the median of the data set.
suppose we need to find the median of data set 5, 7, 23, 21, 15, 30, 17, 27
First, arrange all the values in ascending (smallest to greatest) order as,
5, 7, 15, 17, 21, 23, 27, 30
Now, we have 8 data values (or simply we have 8 numbers in the set), find the middle two numbers of the set,
5, 7, 15, 17, 21, 23, 27, 30
Here, the middle two terms are 17 and 21,
now find the mean of 17 and 21
Here, the middle two terms are 17 and 21,
now find the mean of 17 and 21
\(\frac{17+21}{2}=\frac{38}{2}=19\)
So, 19 is the median of the given data set.
Mode: The data which appears most often in a data set means the value which occurs most number of times in a set, is called the mode of the set.
Example: suppose we have data set 2,7,6,1,11,15,14,2,6,6,7
Arrange the data in ascending order, (this will make question easy), as:
1, 2, 2, 6, 6, 6, 7, 7, 11, 14, 15
In this set the number 6 occurs most number of times (three times) so, the mode of the data set is 6.
Note 1: There may be no mode if no value appears more than any other.
Example: Find the mode of 5, 11, 10, 13, 14, 2, 12, 3
In the above data each values occurs same number of times, so the data has no mode.
Note 2: There may also be two modes (bi-modal), three modes (tri-modal), or four modes or more modes (multimodal).
Example 1: Find the mode of 5, 11, 10, 5, 13, 14, 2, 2, 12, 3
Arrange the data in ascending order as, 2, 2, 3, 5, 5, 10, 11, 12, 13, 14
In the above data set the values 2 and 5 occur more than other values means both 2 and 5 occur 2-times in the data set, therefore this data has two modes 2 and 5.
Example 2: Find the mode of 5, 11, 10, 5, 13, 14, 2, 2, 12, 3, 13
Arrange the data in ascending order as, 2, 2, 3, 5, 5, 10, 11, 12, 13, 13, 14
In the above data set the values 2, 5 and 13 occur more than other values means 2, 5 and 13 occur 2-times in the data set, therefore this data has three modes 2, 5 and 13.
So, a data set can have multi modes.
Range: The ranges of the data set is the difference between the highest and lowest values in the set. To find lowest and highest values, arrange the data in ascending order.
Example: Find the Range of 11, 15, 7, 3, 4, 16, 12, 13
First arrange the data in ascending order as: 3, 4, 7, 11, 12, 13, 15, 16
Highest value = 16 and lowest value = 3
Range =16-3=3
Q: Find mean median, mode and range of 13, 18, 13, 14, 13, 16, 14, 21, 13
Ans: first arrange the data in ascending order as, 13, 13, 13, 13, 14, 14, 16, 18, 21
\({Mean}=\frac{13+13+13+13+14+14+16+18+21}{9}=\frac{263}{9}=15\)
\({Median}=middle\ number\ of\ the\ data=14\)
\({Mode}=the\ value\ which\ occurs\ most\ number\ of\ times\ in\ set=13 \)
\({Range}=highest\ value-Lowest\ value=21-13=8\)
Factorization: Prime Factorization
Before factorization, we need to know that what the factor is...?
Example: The number 2 divides the number 4, therefore 2 is a factor of 4.
The number 3, divides the number 12, therefore 3 is a factor of 12.
Factorization means when we write a number as a product of smaller numbers or the method to breaking down a number into smaller numbers.
Example: The number 20 can be written as the product of smaller numbers as,
\(20=4\times5\),
\(20=2\times10\)
\(20=2\times2\times5\)
So, the numbers 2,4,5 and 10 are the factors of 20.
Prime factorization: This is a method to find which prime numbers multiply together to make the original number.
Example: Suppose we need to find prime factors of 20. 
Start dividing 20 with the smallest prime number which is 2,
we will get \(\frac{20}{2}=10\),
so 20 can be written as \(2\times10\)
But 10 is not a prime number,
Now divide 10 with the smallest prime number, we will get \(\frac{10}{2}=5\),
so 10 can be written as \(2\times5\).
Now 5 is a prime number means we can not divide it further, so by combining these we can say that:
20 can be written as the product of prime numbers 2,2 and 5, these are the prime factors of 20 as:
\(\mathbf{20}=\mathbf{2}\times\mathbf{2}\times\mathbf{5}\)
Another method to find Prime Factors is Factor Tree
Factor tree: This method includes to find any factors of given number and then find factors of those factors till we didn’t get all the prime numbers.
Example: Suppose we need to find prime factors of 108 by using factor tree method.
Take factors of \(108\ =\mathbf{9}\times\mathbf{12}\) and write under 108 
Now find the factors of factors 9 and 12 (which we got in step 1), as:
\(9=\mathbf{3}\times\mathbf{3}\\) and
12=\mathbf{4}\times\mathbf{3}\),
write factors under the numbers 9 and 12.
now 3 is a prime number but not 4, so find factors of 4, as:
4=2\times2
Now we got all the prime factors of 108 as:
\(\mathbf{2}\times\mathbf{2}\times\mathbf{3}\times\mathbf{3}\times\mathbf{3}\)
So, \(\ \mathbf{108}=\mathbf{2}\times\mathbf{2}\times\mathbf{3}\times\mathbf{3}\times\mathbf{3}\)