# Ex.14.2 Q3 Statistics Solution - NCERT Maths Class 9

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## Question

The relative humidity (in $$\%$$) of a certain city for a month of $$30$$ days was as follows:

$$98.1\,\,\, 98.6\,\,\, 99.2\,\,\, 90.3\,\,\, 86.5\,\,\, 95.3\,\,\, 92.9\,\,\, 96.3\,\,\, 94.2\,\,\, 95.1\,\,\, \\89.2\,\,\, 92.3\,\,\, 97.1\,\,\, 93.5\,\,\, 92.7\,\,\, 95.1\,\,\, 97.2\,\,\, 93.3\,\,\, \\95.2\,\,\, 97.3\,\,\, 96.2\,\,\, 92.1\,\,\, 84.9\,\,\, 90.2\,\,\, \\95.7\,\,\, 98.3\,\,\, 97.3\,\,\, 96.1\,\,\, 92.1\,\,\, 89$$

1. Construct a grouped frequency distribution table with classes $$84 - 86, 86–88,$$ etc.
2. Which month or season do you think this data is about?
3. What is the range of this data?

## Text Solution

What is known?

• The relative humidity (in $$\%$$) of a certain city over a month of $$30$$ days.
• Class size is $$2$$, so the class intervals will be $$84-86, 86-88, 88-90$$ and so on.

What is unknown?

• Constructing a grouped frequency distribution table.
• The month / season that the data talks about.
• Range of this data [which is the difference of the highest and the lowest values in the data.]

Reasoning:

By drawing frequency distribution table we can observe data month.

Range of data $$=$$ maximum value $$–$$ minimum value

Steps:

Construct a grouped frequency distribution table with class size of $$2$$

The relation humidity (in $$\%$$) of a certain city for a month can be represented as follows:

 Relative Humidity (in $$\%$$) Number of Days (frequency) $$84-86$$ $$1$$ $$86-88$$ $$1$$ $$88-90$$ $$2$$ $$90-92$$ $$2$$ $$92-94$$ $$7$$ $$94-96$$ $$6$$ $$96-98$$ $$7$$ $$98-100$$ $$4$$ Total $$30$$

The following features can be observed:

• The relative humidity was $$92\%$$ and above, over a period of $$24$$days \begin{align}(\frac{4}{5} \text{of a month})\end{align}
• Since the relative humidity $$\%$$ is very high, it must be a data from a month of rainy season.

\begin{align}\text{Range of data} &= \text{Maximum value} - \text{Minimum value}\\ &= 99.2 – 84.9\\ &= 14.3\end{align}

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