Question

The lengths of the pieces of lumber that a carpenter has are shown in the table.

2 ft 3 ft 6 ft 1.5 ft 4.5 ft 1 ft
3. Find the mean length. 4. Find the median length.

Answer 1

Mean length = 3ft

Median length = 2.5ft

Explanation:

Given the lengths of the pieces of lumber that a carpenter has as shown;

2 ft, 3 ft, 6 ft, 1.5 ft, 4.5 ft, 1 ft

3) The mean length is expressed as the ratio of the sum total of the lengths to the total amount of pieces of lumber given.

Mathematically; Mean (
`\overline x`) =
`(\sum Xi)/(N)`

Xi is the individual length

N is the total amount of pieces of lumber = 6pieces

`\overline x = (2+3+6+1.5+4.5+1)/(6) \\\overline x = (18)/(6) \\\overline x = 3ft`

4) Median is the value at the middle of the given lengths after rearrangement. Rearrangement can either be ascending or descending.

Rearranging the data in ascending order we have;

1ft, 1.5ft, 2ft, 3ft, 4.5ft, 6ft

The two lengths at the middle are 2ft and 3ft. Taking the average of the two values since we cannot have 2 median values.

Median = 2+3/2

median = 2.5ft

Answer 2

The mean length is 3 ft

while the median length is 2.5 ft

Explanation:

The mean length is the sum of the lengths divided by the count of the lengths.

Mathematically, that is;

(2 + 3 + 6 + 1.5 + 4.5 + 1)/6 = 18/6 = 3 ft

To calculate the median length, we first need to rearrange the lengths in increasing order

1, 1.5, 2, 3, 4.5, 6

Now, looking at these lengths, the middle lengths are 2ft and 3ft

we can add both together and divide by 2

That would be (2+3)/2 = 5/2 = 2.5 ft