# Express the quartiles, Q1, Q2, and Q3, of a normally distributed variable in terms of its mean, µ, and standard deviation, σ.

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Express the quartiles, Q1, Q2, and Q3, of a normally distributed variable in terms of its mean, µ, and standard deviation, σ.

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Step 1

First Quartile (Q1)

From the given information the first quartile is represented by 25th percentile and it separates the bottom 25% of the data from the top 75%.

Here, the 25th percentile represents the area of 0.25 to the left of z.

Use the standard normal table to find the area,

Procedure:

• Locate the area of 0.25 in the standard normal table.
• Move let until the first column and notes the value as –0.6.
• Move upward until the top row is reached and note the value as 0.07.

The z-score is –0.67.

The first quartile calculated by

Step 2

Second Quartile (Q2)

The second quartile is represented by 50th percentile and it separates the bottom 50% of the data from the top 50%.

Here, the 50th percentile represents the area of 0.50 to the left of z.

Use the standard normal table to find the area,

Procedure:

• Locate the area of 0.50 in the st...

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