Answer :
The 25th percentile is 166 cm. 50th percentile (median) is 172. the 75th percentile is 184 cm.
How to find the 25th, 50th, and 75th percentile for the given data.
To find the percentiles for the given data, we first need to put the heights in order from smallest to largest:
137, 148, 155, 158, 165, 166, 166, 166, 166, 171, 171, 173, 175, 180, 184, 184, 186, 186, 186, 186
We can see that there are 20 boys in the class, so we can use the following formulas to find the percentiles:
To find the xth percentile, we need to find the value that separates the x% of the data from the rest. This can be found using the formula: x/100 * (n + 1), where n is the number of data points.
If the result of the formula is a whole number, the percentile is the average of that value and the next value in the data set. If the result is not a whole number, we round up to the nearest whole number and take the value in that position.
Using these formulas, we can find the 25th, 50th, and 75th percentiles:
25th percentile: 25/100 * (20 + 1) = 5.25, so we round up to 6. The 6th value in the data set is 166, so the 25th percentile is 166 cm.
50th percentile (median): 50/100 * (20 + 1) = 10.5, so we take the average of the 10th and 11th values in the data set: (171 + 173) / 2 = 172 cm.
75th percentile: 75/100 * (20 + 1) = 15.75, so we round up to 16. The 16th value in the data set is 184, so the 75th percentile is 184 cm.
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