Question

The time taken (in hours) by 11social worker to clean locality are as follows 7,6,5,6,5,7,8,6,8,7,6. Find mean, median and mode for the data? plz answer fast

Answer 1

Solution!!

Observations = 7, 6, 5, 6, 5, 7, 8, 6, 8, 7, 6

The first thing which we have to do is arrange the observations in ascending order.

Observations = 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8

Total number of observations = 11

Let's find out the mean first.

→ Mean = (Sum of all observations) ÷ (Total number of observations)

→ Mean = (5 + 5 + 6 + 6 + 6 + 6 + 7 + 7 + 7 + 8 + 8) ÷ (11)

→ Mean = (71) ÷ (11)

Mean = 6.45

Now, we're gonna find the median. There are different ways to find the median. 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. In this case, the number of observations is 11. So, we will use the formula to find the median of odd number of observations.

→ Median = ((n + 1)/2)th term

Here n is the total number of observations.

→ Median = ((11 + 1)/2)th term

→ Median = ((12)/2)th term

→ Median = 6th term

As we see, the sixth term of the observations which are in ascending order is the median.

Median = 6

Mode is the value which is occurring the most in the observations.

5 is occurring 2 times.

6 is occurring 4 times.

7 is occurring 3 times.

8 is occurring 2 times.

So, 6 is the value which is occurring the most in the observations.

Mode = 6

Answer 2

Solution

~Mean is defined as the average or central value

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It is given as :-

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${\underline{\boxed{\sf{\color{grey}{\bull \:mean=\frac{sum \: of \: observations}{no\:.of \: observation}}}}}}$

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$\sf{ \to sum \: of \: observations= 7+6+5+6+5+7+8+6+8+7+6}$

$\sf{ \to sum \: of \: the \:observations =71}$

$\sf{ \to\:No\: .of \:observation= 11}$

$\sf{ \implies \: Mean = \frac{71}{11}} \\ \\\sf{ \implies \: \red{Mean = 6.45}}$

✏️Therfore mean is 6.45.

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Now, let us find the median of the given data.

~Median is defined as a value of a variable which divides the data into two equal parts.

~the first most important step to obtain the median is that data should be arranged in an ascending or descending order.

$\mathtt{ \bull\:Ascending\:order} \\\pink{5,5,6,6,6,6,7,7,7,8,8}$

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Condition for individual series:-

⇝If the value of N is odd then simply the value of median is:-

$\mathtt{ \to \frac{(N+1)}{2}^{th}term}$

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⇝If the value of N is even, then the formula is :-

$\mathtt{Median = \frac{[ size\:of \: \frac{N}{2} \: term + \: size \: of \: (\frac{N}{2} + 1)^{th} \:term]}{2}}$

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Here the n= 11, which means odd.

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$\sf{ \implies Median = \frac{11+1}{2}} \\ \\ \sf{ \implies \: Median= \frac{12}{2}} \\ \\ \sf{ \implies \color{red}median= 6^{th } term }$

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✏️So 6th term is the median of the given data and 6th term is 6.

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Now let us find the mode of the given data.

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~The observation Which has the highest frequency in data is called Mode.

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Data️️️️️ ⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀Frequency

5️️️️️️️️⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀2

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6️️️️️️️️⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀4

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7️️️️️️️️⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀3

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8️️️️️️️️⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀⠀⠀⠀⠀️️️️️️⠀️️️️️️2

_______________________

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We observe that 6 has the highest frequency as 4.

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✏️So 6 is the mode of the given data.

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