Question

21. The number of road accidents reported in a city in the months of a
year are: 56, 28, 90, 15, 73, 81, 60, 23, 45, 36, 51, 77. Calculate the
mean and range for the given data.
​

Answer 1

$\sf\purple{Answer}$

$\sf\underline\purple{Given:-}$ The road accidents reported months of a year are

• 56, 28, 90, 15, 73 , 81 , 60 , 23 , 24 , 36 , 51 ,77

$\sf\underline\purple{To\: find :- }$

• Mean of data , Range of data

$\sf\underline\purple{Formulae\:to\:know}$

Mean = $\sf\dfrac{Sum\:of\:observations}{No\:of\:observations}$

Range = Highest value - Lowest value

________________________________________

$\huge\bf{Solution}$

$\sf\underline\purple{Finding\:mean}$

Sum of observations = 56+ 28+ 90+ 15+73 + 81 + 60+ 23 + 45, + 36 + 51+ 77.

Sum of observations = 635

No.of observations = 12

Mean = $\sf\dfrac{Sum\:of\:observations}{No\:of\:observations}$

Mean = $\sf\dfrac{635}{12}$

$\sf\purple{Mean}$ = 52.91

$\sf\underline\purple{Finding\:Range}$

Highest value in data = 90

Lowest value in data = 15

Range = Highest value - Lowest value

Range = 90-15

$\sf\purple{Range}$ = 75

So, mean of data is 52.91, Range of data is 75

Answer 2

Solution :

$\: \:$

Here

• Sum of observations = 56 + 28 + 90 + 15 + 73 + 81 + 60 + 23 + 45 + 36 + 51 + 77
• Number of observations = 12

$\:$

For finding the mean of the given data we've to find the ratio of sum of observations to the number of observations.

$\: \:$

$\star\underline{\boxed{\sf\pink{Mean = \frac{sum \: of \: observations}{number \: of \: observations} }}}$

$\: \:$

$\mathfrak{ \underline{ \bigstar \: substituting \: the \: values \: : }}$

$\: \:$

$\sf:\implies \: mean = \dfrac{sum \: of \: observations}{number \: of \: observations}$

$\:$

$\sf:\implies mean \: = \dfrac{56 + 28 + 90 + 15 + 73 + 81 + 60 + 23 + 45 + 36 + 51 + 77}{12}$

$\:$

$\sf : \implies \: mean = \dfrac{635}{12}$

$\:$

$\sf : \implies \: \underline{\boxed{\mathfrak\purple{mean = 52.91}}} \: \bigstar$

$\:$

$\sf\therefore{\underline{Hence, \: the \: mean \: of \: the \: observation \: is \: \bold{52.91}.}}$

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$\: \:$

Now we'll find the range of the data. For finding the range of the given data, we'll subtract the minimum value from the maximum value.

$\: \:$

Here

$\:$

• Maximum value = 90
• Minimum value = 15

$\: \:$

$\star \: \underline{\boxed{\sf\pink{Range = maximum \: value \: - \: minimum \: value}}}$

$\: \:$

$\mathfrak {\underline{ \bigstar \: substituting \: the \: values \: : }}$

$\:$

$\sf :\implies \: Range = maximum \: value \: - \: minimum \: value$

$\:$

$\sf :\implies \: Range =90 - 15$

$\:$

$\sf :\implies \: \underline{\boxed{\mathfrak\purple{Range =75}}} \: \bigstar$

$\:$

$\sf\therefore{\underline{Hence, \: the \: range \: of \: the \: data \: is \: \bold{75}.}}$

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