In a data set, the first quartile (Q1) marks the 25th percentile, and the third quartile (Q3) marks the 75th percentile. The interquartile range (IQR) is the range between Q1 and Q3.
To find the number of values between the first and third quartile in a data set of 300 values, you can determine how many values lie between these two quartiles.
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The first quartile (Q1) corresponds to the 25th percentile, which means 25% of the data points are below Q1. In a dataset of 300 values, this means: \[ 0.25 \times 300 = 75 \text{ values are below Q1} \]
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The third quartile (Q3) corresponds to the 75th percentile, which means 75% of the data points are below Q3. Thus: \[ 0.75 \times 300 = 225 \text{ values are below Q3} \]
To find the number of values between Q1 and Q3, subtract the number of values below Q1 from the number of values below Q3: \[ 225 - 75 = 150 \]
Therefore, there are 150 values between the first quartile and the third quartile in a data set of 300 values.
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