Sand and clay studies were conducted at a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded.   22.8 30.1 26.4 20.5 23.5 22.2 ​ 23.7 28.4 28.1 29.0 28.6 24.0 ​ Convert this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median.

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Sand and clay studies were conducted at a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded.
 

22.8

30.1

26.4

20.5

23.5

22.2

23.7

28.4

28.1

29.0

28.6

24.0

Convert this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median.

Expert Solution
Step 1-Median

The twelve consecutive depth are: 22.8, 30.1, 26.4, 20.5, 23.5, 22.2, 23.7, 28.4, 28.1, 29.0, 28.6, 24.0

To convert the above sequence of numbers to a sequence of symbols A and B, the median is required. 

To find the median of the above numbers, arrange them in ascending (increasing) order. 

Ascending order: 20.5, 22.2, 22.8, 23.5, 23.7, 24.0, 26.4, 28.1, 28.4, 28.6, 29.0, 30.1

Since the number of observations (n) is equal12 (even number) the formula for median will be :

Statistics homework question answer, step 1, image 1

Note: The observations need to be selected from ascending order.

Here, n=12 therefore,

Statistics homework question answer, step 1, image 2 

Statistics homework question answer, step 1, image 3

Here, 6th observation is 24.0 and 7th observation is 26.4. in the ascending order.

Therefore the median will be: 

Statistics homework question answer, step 1, image 4

The value of the median is 25.2 for the above sequence. 

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