Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

In a continuous series, if [tex]\bar{X} = 20[/tex], [tex]fx = 420[/tex], and [tex]N = 18 + 2a[/tex], find the value of [tex]a[/tex].

Sagot :

To find the value of [tex]\( a \)[/tex], given the mean [tex]\(\bar{X} = 20\)[/tex], the sum of the products of frequencies and their corresponding values [tex]\( \sum fx = 420 \)[/tex], and the total number of observations [tex]\( N = 18 + 2a \)[/tex], we can follow these steps:

1. Understand the given formula for the mean:
The formula for the mean ([tex]\(\bar{X}\)[/tex]) of a frequency distribution is:
[tex]\[ \bar{X} = \frac{\sum fx}{N} \][/tex]

2. Substitute the given values:
Given [tex]\(\bar{X} = 20\)[/tex] and [tex]\(\sum fx = 420\)[/tex], we substitute these into the formula:
[tex]\[ 20 = \frac{420}{18 + 2a} \][/tex]

3. Solve for [tex]\( N \)[/tex]:
Multiply both sides of the equation by [tex]\( (18 + 2a) \)[/tex] to isolate the total number of observations:
[tex]\[ 20 (18 + 2a) = 420 \][/tex]

4. Expand the equation:
[tex]\[ 20 \times 18 + 20 \times 2a = 420 \][/tex]

Simplify the terms:
[tex]\[ 360 + 40a = 420 \][/tex]

5. Isolate the term with [tex]\( a \)[/tex]:
Subtract 360 from both sides of the equation:
[tex]\[ 40a = 420 - 360 \][/tex]

Simplify the right-hand side:
[tex]\[ 40a = 60 \][/tex]

6. Solve for [tex]\( a \)[/tex]:
Divide both sides by 40:
[tex]\[ a = \frac{60}{40} = 1.5 \][/tex]

So the value of [tex]\( a \)[/tex] is [tex]\( 1.5 \)[/tex].