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Standard X

Mathematics

Class Interval

To find out t...

Question

To find out the concentration of SO₂ in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below:

Concentration of SO₂ (in ppm) Frequency

0.00−0.04
0.04−0.08
0.08−0.12
0.12−0.16
0.16−0.20
0.20−0.24 4
9
9
2
4
2

Find the mean of concentration of SO₂ in the air.

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Solution

Let the assumed mean A = 0.1 and h = 0.04.

We know that mean,

Now, we have.

Putting the values in the above formula, we have

$= 0.10 + 0.04 [\frac{1}{30} \times (- 1)] = 0.10 - \frac{0.04}{30} = 0.10 - 0.001 = 0.099$

Hence, the mean concentration of SO₂in the air is 0.099 ppm.

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Question 7
To find out the concentration of $S O_{2}$ in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below:

$\begin{matrix} Concentration of S O_{2} (in pmm) & Frequency 0.00 - 0.04 & 4 0.04 - 0.08 & 9 0.08 - 0.12 & 9 0.12 - 0.16 & 2 0.16 - 0.20 & 4 0.20 - 0.24 & 2 \end{matrix}$

Find the mean concentration of $S O_{2}$ in the air.

Q. To find out the concentration of

S O_{2}

in the air (in parts per million, i.e., ppm), the data was collected for

30

localities in a certain city and is presented below:

Concentration of $S O_{2}$ (in ppm)	Frequency
$0.00 - 0.04$	$4$
$0.04 - 0.08$	$9$
$0.08 - 0.12$	$9$
$0.12 - 0.16$	$2$
$0.16 - 0.20$	$4$
$0.20 - 0.24$	$2$

Find the mean concentration of

S O_{2}

in the air.

Q. To find out the concentration of

{S O}_{2}

in the air (in parts per million, i.e.,

p p m

), the data was collected for

30

localities in certain city and is presented below:

Concentration of ${S O}_{2}$ (in ppm)	Frequency
$0.00 - 0.04$	$4$
$0.04 - 0.08$	$9$
$0.08 - 0.12$	$9$
$0.12 - 0.16$	$2$
$0.16 - 0.20$	$4$
$0.20 - 0.24$	$2$

Find the mean concentration of

{S O}_{2}

in the air.

Concentration of SO₂ (in ppm)	Number of days (frequency )
0.00 − 0.04	4
0.04 − 0.08	9
0.08 − 0.12	9
0.12 − 0.16	2
0.16 − 0.20	4
0.20 − 0.24	2
Total	30

The above frequency distribution table represents the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days. Using this table, find the probability of the concentration of sulphur dioxide in the interval 0.12 − 0.16 on any of these days.

Given below is the concentration of SO₂ in air (in ppm = parts per million) in 30 localities:
$\begin{matrix} S O_{2} concentration (in ppm) & Number of localities 0.00 - 0.04 & 4 0.04 - 0.08 & 9 0.08 - 0.12 & 9 0.12 - 0.16 & 2 0.16 - 0.20 & 4 0.20 - 0.24 & 2 \end{matrix}$
Find the mean of $S O_{2}$ concentration using assumed - mean method.

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Concentration of SO₂ (in ppm)	Frequency
0.00−0.04 0.04−0.08 0.08−0.12 0.12−0.16 0.16−0.20 0.20−0.24	4 9 9 2 4 2

Let the assumed mean A = 0.1 and h = 0.04. We know that mean, Now, we have. Putting the values in the above formula, we have =0.10+0.04130×-1=0.10-0.0430=0.10-0.001=0.099 Hence, the mean concentration of SO2 in the air is 0.099 ppm.

Let the assumed mean A = 0.1 and h = 0.04.

We know that mean,

Now, we have.

Putting the values in the above formula, we have

$= 0.10 + 0.04 [\frac{1}{30} \times (- 1)] = 0.10 - \frac{0.04}{30} = 0.10 - 0.001 = 0.099$

Hence, the mean concentration of SO₂in the air is 0.099 ppm.