Chapter: – Data Handling

Topic: – Mean, Median, and Mode

In mathematics Mean, Median and Mode are three different measures of centre for a dataset. The main motive of using Mean, Median and Mode is to summarize large datasets with a single number in order to represent typical data points from the large dataset.

What is Mean?

It is defined as the average number from the given dataset. The mean data set is calculated by adding all the digits with a total number of digits. The formula which is used for calculation for Mean is,

Mean (x̄) = ∑ x_i / n

For Example – There are 10 numbers ranging from 1 to 10 and we have to calculate the Mean.

Mean = Sum of digits / Total number of digits

Mean = 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 / 10

• 55/10
• 5

What is Median?

Median is a process for finding out the middle number by ordering all the digits in a serial manner and finding the number which is in the middle.  The median of series of numbers is calculated using the formula, (n + 1)/2.

For example – there are 11 numbers ranging from 1 to 11 and we have to find out the median from series 1 to 11.

Number Series is 1, 2, 3, 4, 5, 6, 7, 8, 9 ,10, 11.

Using formula (n + 1)/2, we get

• (11 + 1)/2
• 12/2 è 6

Therefore, we get Median as 6.

In Median, if the number is odd then the formula is, Median = (n + 1/2) th term

if the number is even then the formula is, Median = ((n/2)th term + (n/2+1)th term)/2

What is Mode?

The mode is the process of finding out the number which occurs several times in the given series of sets. The number which is repeated most of the time is considered as the mode. For example:

There are 10 numbers in a set and we have to find out the mode from the set.

Numbers are: – 1,2,3,3,3,4,4,4,5,3

In the series, one can see that 3 is repeated 4 times and 4 is repeated 3.

Therefore, the mode in a given series of number will be 3 because it is repeated 4 times as compared to another number.

Mode è 3

Quiz

1. Find the Mean of the following series number?

1,2,3,4,5,6, 7

1. 1
2. 2
3. 3
4. 4

Answer: – 4, is the correct answer.

The formula which is used for calculation of Mean = Sum of digits / Total number of digits

Mean = 1 + 2 + 3 + 4 + 5 + 6 + 7 / 7

• 28/7
• 4

2. Find the mode from following number?
   1,1,1,1,5,5,3,4,5,8,6,4,5,5,6,6,1
3. 5
4. 3
5. 4
6. 1

Answer: – 1, is the correct answer because is in this series 1 is repeated highest time in series that is 5 times.

3. Calculate Median from the given series?

1,2,3,4,5,6,7

1. 1
2. 4
3. 3
4. 2

Answer: – 4, is the median.

Therefore, using formula (n + 1 / 2), we get

• (7 + 1) / 2
• 8/2 è 4

Hence, 4 is the median.

4. In a cricket match if 5 players have scored 45, 96, 20, 45 and 41 respectively. Then, find out the Mean of runs scored?
5. 4
6. 2
7. 6
8. 8

Answer: – 49.4, is the correct answer.

Average run scored = Total number of run scored by 5 players / Total number of players

• 45 + 96 + 20 + 45 + 41 / 5
• 247/5
• 4

5. What is the median of following number set?

1,1,2,3,6,8,10,11,12,15,30

1. 1
2. 6
3. 8
4. 12

Answer: – 8, is the correct answer.

As, one can see that, the number series in sorted form as it is in increasing order.

Therefore, in this case the Median of number is 8.

6. Calculate mean from the following values

10, 12, 11, 6, 8, 9, 4, 1

7. 223
8. 200
9. 625
10. 425

Answer: – 7.625, is the correct answer.

One has to firstly, find out sum of all the numbers. Therefore, we get

• 10 + 12 + 11 + 6 + 8 + 9 + 4 + 1
• 61

Here, total number of digits are 8.

Now, with use of Mean formula, that is

Mean = Sum of all the numbers / Total number of digits

Therefore, we get

Mean = 61 / 8

Mean = 7.625

7. From the following table, one can see the daily income of 5 workers. Now, from the data given in the table find out the Mean?

762. 5
763. 5
764. 5
765. 5

Answer: – 862.5, is the correct answer.

Total number of workers = 4

Sum of income of all workers = 800 +900+ 950 + 800

• 3450

Therefore, Mean = Total number of worker / Sum of their income

• 3450 /4
• 5

8. What is the symbol of Mean?
9. ∑
10. Ω
11. Π
12. x̄

Answer: – x̄, is used for the representation of Mean.

9. What does this symbol mean Σ x_i?
10. Sum of all the numbers in the set
11. Sum of first two number
12. Addition of first two number
13. Multiplication of all numbers

Answer: – Sum of all the numbers in the set, is the correct answer.

10. Find mode of following numbers

1,2,3,4,5,6,7,8,9,9,8,7,4,5,6,3,4,1,5,6,3,2,5,4,7,8,9,4,5,4,4,5,5,6,4

1. 1
2. 2
3. 4
4. 6

Answer: – 4, is the correct answer because in the series of number 4 is repeated by 8 times.