Find the median of the following data set.
1 ¹/₄, 5/8, 3/5, 1/2, 1 ¹/₂, 1 ³/₄

Solution:

Given, the data is 1 ¹/₄, 5/8, 3/5, 1/2, 1 ¹/₂, 1 ³/₄.

We have to find the median of the given data set.

The median is the central number of a data set.

To find the median, we have to arrange the data values from lowest to highest value.

If the total number of given data is odd, then median is the middle number.

If the total number of given data is even, then median is the mean of the two middle numbers. i.e., add two middle numbers and divide them by two.

1 ¹/₄ = (4 + 1)/4 = 5/4

1 ¹/₂ = (2 + 1)/2 = 3/2

1 ³/₄ = (4 + 3)/4 = 7/4

Now, the data is 5/4, 5/8, 3/5, 1/2, 3/2, 7/4.

Taking LCM of the numerator,

LCM of 4, 8, 5, 2, 2, 4

LCM = 2 × 2 × 2 × 5

= 40

The data can be written as 50/40, 25/40, 24/40, 20/40, 60/40, 70/40.

Arranging the data in ascending order,

20/40, 24/40, 25/40, 50/40, 60/40, 70/40

The fractions arranged in order from lowest to highest value are 1/2, 3/5, 5/8, 5/4, 3/2, 7/4.

Total number of given data = 6

This implies that the total number of given data is even.

Median = [(5/8) + (5/4)]/2

= [(5 + 10)/8]/2

= [15/8]/2

= 15/16

Therefore, the required median is 15/16.

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Find the median of the following data set. 1 1/4, 5/8, 3/5, 1/2, 1 1/2, 1 3/4

Summary:

The median of the following data set: 1 1/4, 5/8, 3/5, 1/2, 1 1/2, 1 3/4 is 15/16.