Question
Asked Jan 21, 2020
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Find the 5 number summary of the following set of data: 11, 8, 12, 4, 7, 10, 3, 15, 8, 8, 7

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Expert Answer

Step 1

In general, five number summary represents minimum, first quartile, median, third quartile and maximum.

Step 2

The data points is arranged in ascending order as follows:

3, 4, 7, 7, 8, 8, 8, 10, 11, 12, 15.

Minimum and maximum:

In this case, the minimum and maximum values are 3 and 15.

Median.

The median of the dataset is nothing but the second quartile of dataset.

The data points is arranged in ascending order as follows:

3, 4, 7, 7, 8, 8, 8, 10, 11, 12, 15.

The number of observations in the dataset is n = 11.

Since, 11 is an odd number, the median of the data will be the middle observation of the ordered dataset.

Here, the middle observation of the dataset is 8. Therefore, the median is 8.

First quartile:

The general procedure to obtain first quartile is,

  • Arrange the data in ascending order.
  • Obtain the value of c = (n/4).
  • If the value of c is not a whole number, then round the value of c to the next whole number. The cth term in the ordered dataset is the first quartile of the dataset.
  • If the value of c is a whole number, then the first quartile is the average of cth and (c+1)th term in the ordered data set.

The first quartile is obtained as follows:

Statistics homework question answer, step 2, image 1
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Step 3

Third quartile:

The general procedure to obtain third quartile is,

  • Arrange the data in ascending order.
  • Obtain the value of c = (3n/4).
  • If the value of c is not a whole number, then round the value of c to the next whole number. The cth term in the ordered dataset is the third quartile of the dataset.
  • If the...
Statistics homework question answer, step 3, image 1
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