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QuestionFind the 75th percentile of the data set: 14, 11, 15, 14, 17, 15, 16, 14, 11, 13. Options: 13.75, 14.25, 14.75, 15.25.

Studdy Solution

STEP 1

Assumptions1. The data set is {14,11,15,14,17,15,16,14,11,13} . The data set is not sorted3. We need to find the75th percentile

STEP 2

First, we need to sort the data set in ascending order.
Sorted data set={11,11,13,14,14,14,15,15,16,17}\text{Sorted data set} = \{11,11,13,14,14,14,15,15,16,17\}

STEP 3

Next, we need to find the index of the75th percentile. We can do this by multiplying the total number of data points by0.75.
Index=Total number of data points×0.75\text{Index} = \text{Total number of data points} \times0.75

STEP 4

Now, plug in the total number of data points into the formula to find the index.
Index=10×0.75\text{Index} =10 \times0.75

STEP 5

Calculate the index.
Index=10×0.75=7.5\text{Index} =10 \times0.75 =7.5

STEP 6

Since the index is not a whole number, the75th percentile is the average of theth and8th data points in the sorted set.
75th percentile=th data point+8th data point2\text{75th percentile} = \frac{\text{th data point} + \text{8th data point}}{2}

STEP 7

Plug in the7th andth data points into the formula to find the75th percentile.
75th percentile=15+152\text{75th percentile} = \frac{15 +15}{2}

STEP 8

Calculate the75th percentile.
75th percentile=15+152=15\text{75th percentile} = \frac{15 +15}{2} =15The75th percentile is15.

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