Question

The scores in science test of 11 students is as follows:

25, 20, 19, 15, 12, 21, 20, 10, 15, 20, 10

Find the mean, median and mode of this data. Are they same?​

Answer 1

Step-by-step explanation:

Given:-

The scores in science test of 11 students is as follows:

25, 20, 19, 15, 12, 21, 20, 10, 15, 20, 10

To find:-

Find the mean, median and mode of this data. Are they same?

Solution:-

i)Mean:-

Given observations are

25, 20, 19, 15, 12, 21, 20, 10, 15, 20, 10

Sum of all observations =

25+ 20+19+15+12+21+20+10+15+20+10=187

Number of all observations = 11

We know that

Mean=Sum of all observations/Number of all observations

=>Mean = 187/11

Mean = 17

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ii)Median:-

Given observations are

25, 20, 19, 15, 12, 21, 20, 10, 15, 20, 10

On writing them into ascending order then

=>10,10,12,15,15,19,20,20,20,21,25

Number of observations = 11

11 is an odd number

We know that

The number of observations is 'n' ,an odd number then the median of the data is (n+1)/2 th observation.

We have ,n=11

(n+1)/2=(11+1)/2=12/2=6

6th observation of the data = 19

Median = 19

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iii)Mode:-

Given observations are

25, 20, 19, 15, 12, 21, 20, 10, 15, 20, 10

On writing them into ascending order then

=>10,10,12,15,15,19,20,20,20,21,25

We know that The mode is the most frequently occuring observation of the given data

20 occurs 3 times

Mode = 20

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Answer:-

i)Mean of the given data = 17

ii)Median of the given data = 19

iii)Mode of the given data = 20

iv)Mean ,Median and Mode are not same for the given data.

Used formulae:-

• Mean=Sum of all observations/Number of all observations.

• The number of observations is 'n' ,an odd number then the median of the data is (n+1)/2 th observation.

• The mode is the most frequently occuring observation of the given data