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

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*c*^{th}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*c*^{th}and (*c*+1)^{th}term in the ordered data set.

The first quartile is obtained as follows:

Step 3

**Third quartile:**

The general procedure to obtain third quartile is,

- Arrange the data in ascending order.
- Obtain the value of
*c*= (3*n*/4)*.* - If the value of
*c*is not a whole number, then round the value of*c*to the next whole number. The*c*th term in the ordered dataset is the third quartile of the dataset. - If the...

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