Certainly! Let's solve this step-by-step:
Given:
- The mean, [tex]\(\bar{x}\)[/tex], is 10.
- The sum of the product of frequency and the corresponding value (denoted as [tex]\(\Sigma fm\)[/tex]) is 200.
- The number of terms, [tex]\(n\)[/tex], is given by the expression [tex]\( \frac{10}{2 \cdot 3} \)[/tex].
To determine the value of [tex]\(n\)[/tex], we simply evaluate the given expression:
1. Start with the expression for [tex]\(n\)[/tex]:
[tex]\[ n = \frac{10}{2 \cdot 3} \][/tex]
2. Calculate the denominator:
[tex]\[ 2 \cdot 3 = 6 \][/tex]
3. Now, divide the numerator by the denominator:
[tex]\[ n = \frac{10}{6} \][/tex]
4. Simplifying the fraction, we get:
[tex]\[ n = \frac{10}{6} = 1.6666666666666667 \][/tex]
So, the value of [tex]\(n\)[/tex] is approximately 1.6667.
Therefore, the values are:
- Mean ([tex]\(\bar{x}\)[/tex]) = 10
- Sum of [tex]\(fm\)[/tex] ([tex]\(\Sigma fm\)[/tex]) = 200
- Number of terms ([tex]\(n\)[/tex]) = 1.6666666666666667
