Question

Mathematics Question :-

(Class 9, Chapter - Statistics.)

In a mathematics test given to 15 students, the following marks (out of 100) are recorded as follows :-

41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60.

Find the mean, median and mode of this given data.

$\bf\red{Explanation\:Required}$
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Answer 1

$\bullet \:\sf \green{Mean = \frac{Sum \: of \: all \: observations}{Number \: of \: observations} }$

$\sf{Mean = \frac{41 \: + \: 39 + \: 48 + \: 52 + \: 46 + \: 62 + \: 54 + \: 40 + \: 96 + \: 52 + \: 98 + \: 40 + \: 42 + \: 52 + \: 60}{15} }$

$\sf{Mean = \frac{ \cancel{822}}{ \cancel {15}} } {}^{ \: 54 .8}$

________________....

Arranging the data in ascending order :-

39,40,40,41,42,46,48,52,52,52,54,60,62,96,98

Here n = 15 [Odd]

$\bullet\:\sf \green{Median = (\frac{n}{2} + 1)}{}^ \green{th \: term}$

$\sf{ = \frac{15 + 1}{2} }$

$\sf{ = \cancel\frac{16}{2} \: {}^{8} }$

$\sf{ = 8th \: term}$

.°. Value of 8th term = 52

________________...

Mode = 52

Answer 2

Answer:-

Mean = 54.8

Mode = 52

Median = 52

Step by step explanation-

Learn few things before solving any question related to mean, median and mode,

Mean-

$\rm\orange {Mean = \frac{sum \: of \: the \: given \: observations}{number \: of \: the \: \: observations}}$

___....

Median-

When n is odd-

[ n is the number of observations]

$\rm\orange {Median = ( \frac{n + 1}{2} ){}^{th \: observation}}$

When n is even-

$\rm\orange {Median = \frac{1}{2} [( \frac{n}{2} ) {}^{th \: observation} + ( \frac{n}{2} + 1) {}^{value \: of \: observation}]}$

____...

Mode-

$\rm\orange{Mode = most \: frequent \: observation}$

______...

Solutions-

$\huge\bf\blue { For \: Mean}$

Sum of all observations = 41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60 = 822

Number of observations = 15

We know,

$\bf\red {Mean = \frac{sum \: of \: the \: given \: observations}{number \: of \: the \: \: observations}}$

$\rm\blue {Mean = \frac{822}{15} = 54.8}$

_______...

$\huge\bf\blue { For \: Median}$

Arranging the data in ascending order, we get-

39,40,40,41,42,46,48,52,52,52,54,60,62,96,98

As, total number of observations is 15, which is odd. We'll use this formula-

• $\bf\red {Median = (\frac{n + 1}{2} ){}^{th \: observation}}$

$\rm\blue {Median = \frac{15 + 1}{2} = \frac{16}{2} = 8 \: }$

So, 8th observation of the given observations is the median.

39,40,40,41,42,46,48,52,52,52,54,60,62,96,98

52 is median of the given observations.

__________....

$\huge\bf\blue { For \: Mode}$

Arrange the data in ascending order-

39,40,40,41,42,46,48,52,52,52,54,60,62,96,98

We know,

$\bf\red {Mode = most \: frequent \: observation}$

As, 52 is the number which has come most frequently, so of the given observation is 52.

__________________________________________