Question

find the mean median and mode of the data for 4,6,3 ,5,0,6,2, 1,6,1.​

Answer 1

Solution!!

Observations → 4, 6, 3, 5, 0, 6, 2, 1, 6, 1

We have to arrange the above observations in ascending order.

Observations → 0, 1, 1, 2, 3, 4, 5, 6, 6, 6

Number of observations = 10

We have to find the mean, median and mode of the above observations.

Mean = Sum of observations ÷ Number of observations

Mean = (0 + 1 + 1 + 2 + 3 + 4 + 5 + 6 + 6 + 6) ÷ (10)

Mean = 34 ÷ 10

Mean = 3.4

As we can see, the number of observations is 10 which is an even number. The formula to find the median of odd number of observations is different from the formula to find the median of even number of observations. Here, we will use the formula to find the median of even number of observations.

Median = ((n/2)th term + ((n/2) + 1)th term) ÷ 2

Here n is the number of observations.

Median = ((10/2)th term + ((10/2) + 1)th term) ÷ 2

Median = (5th term + 6th term) ÷ 2

The 5th and the 6th term are 3 and 4, respectively.

Median = (3 + 4) ÷ 2

Median = 7 ÷ 2

Median = 3.5

Mode is the observation which occurs the most.

Mode = 6

Answer 2

${ \textbf{ \textsf{ \underline{ \underline{✢Question}}}}} :$

• Find the mean median and mode of the data for 4,6,3 ,5,0,6,2, 1,6,1.

${ \textbf{ \textsf{ \underline{ \underline{✢Answer}}}}} :$

• Required Mode :- 6
• Required Mode :- 6Required Median :- 3.5
• Required Mode :- 6Required Median :- 3.5Required Mean :- 3.4

${ \textbf{ \textsf{ \underline{ \underline{✢Given \: Information}}}}} :$

• Data :- 4,6,3,5,0,6,2,1,6,1.

${ \textbf{ \textsf{ \underline{ \underline{✢Need \: To \: Observe}}}}} :$

• Median,Mode and Mean of the given data

${ \textbf{ \textsf{ \underline{ \underline{✢Basic \: Facts}}}}} :$

• Mean is one of the representative data
• Mode is a highest occuring data often
• Median is the middle value of the data

${ \textbf{ \textsf{ \underline{ \underline{✢Solution}}}}} :$

Mode:-

• Firstly, we may arrange the data into ascending order

⇢$\rm \: 0 < 1 < 1 < 2 < 3 < 4 < 5 < 6 < 6 < 6$

• As Arranging to Ascending order, we will find the most occuring Frequently data .

• As the most occuring data is 6

Median :-

• As we know that median occurs at the middle.
• But the total observation are given in even number .
• By taking two middle value, we can find the required median.

• Two middle value = 3 and 4
• By adding it, we may get 7
• By dividing by 2 , thus median =3.5

Mean:-

• As finding mean, we will divide number of data and total number of data.
• As using required formula, we may find mean

⇢$\sf \: mean = \frac{sum \: of \: observation}{no \: of \: observation}$

$= \frac{ 4 + 6 + 3 + 5 + 0 + 6 + 2 + 1 + 6 + 1.</p><p>}{10}$

$= \frac {34}{10} \\ \\ = 3.4$