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
\({Mean}=\frac{13+13+13+13+14+14+16+18+21}{9}=\frac{263}{9}=15\)
\({Median}=middle\ number\ of\ the\ data=14\)
\({Mode}=the\ value\ which\ occurs\ most\ number\ of\ times\ in\ set=13 \)
\({Range}=highest\ value-Lowest\ value=21-13=8\)