Question

Q3. A sample of single persons in Towson, Texas, receiving Social Security payments
revealed these monthly benefits: $852, $598, $580, $1,374, $960, $878, and $1,130.
(a) What is the median monthly benefit?
(b) How many observations are below the median? Above it?

Answer 1

Solution :

a) To obtain the median follow the given steps :

1) Sort the data in ascending or descending order.

2) If number of observations (n) is an odd number then,

Median = ((n+1)/2)th observation of sorted data.

If number of observations (n) is an even number then,

Median = Arithmetic mean of two middle observation of sorted data.

The given monthly benefits are as follows :

$852, $598, $580, $1,374, $960, $878, and $1,130.
Now we shall sort the data in ascending order, which will be as follows :

$580, $598, $852, $878, $960, $1130, $1374

The number of observations (n) = 7, which is an odd number.

Therefore, median = (7+1)/2 = 4th observation of sorted data.

4th observation of sorted data is $878, therefore median monthly benefit is $878.

Median monthly benefit is $878.

b) Median is interpreted as follows :

50% of the observations of the given data set lie below the median value and 50% of the observations of the given data set lie above the median value.

Hence, 50% of the observations are below the median and 50% of the observations are above the median.

In numbers,

3 observations are below the median and 3 observations are above the median.

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