In a history class there are 25 freshman, 21 sophomores, and 18 juniors. If the freshman averaged 81 on an examination, the sophomores averaged 84, and the juniors averaged 72, find the mean grade for the entire class. (round to the tenths, if necessary)

#### Solution

Given that `$n_1=25$`

(Number of freshman), `$n_2= 21$`

(number of sophomores), `$n_3=18$`

(number of juniors).

`$\overline{x}_1=81$`

average of freshman in an examination, `$\overline{x}_2=84$`

average of sophomores in an examination and `$\overline{x}_3=72$`

average of juniors in an examination.

The mean grade for the entire class is

` $$ \begin{aligned} \overline{x} &=\frac{n_1\overline{x}_1+n_2\overline{x}_2+n_3\overline{x}_3}{n_1+n_2+n_3}\\ &=\frac{25\times 81+21\times 84+18\times 72}{25+21+18}\\ &=\frac{5085}{64}\\ &=79 \end{aligned} $$ `

Thus the mean grade for the entire class is `$79$`

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#### Further Reading

- Statistics
- Descriptive Statistics
- Probability Theory
- Probability Distribution
- Hypothesis Testing
- Confidence interval
- Sample size determination
- Non-parametric Tests
- Correlation Regression
- Statistics Calculators