calculating the frequency of a statistical series
| grade n | `0<=n<4` | `4<=n<8` | `8<=n<12` | `12<=n<16` | `16<=n<=20` |
|---|---|---|---|---|---|
| Number of students | 8 | 5 | 1 | ? | 6 |
1. What is the number of students having obtained a mark between 12 and 16 (excluding 16).
2. How many students got less than 12?
Arithmetic mean
For any series`(x_1, ..., x_n)` of real numbers, we define its arithmetic mean by the formula : `bar x= 1/n sum_(i=1)^n x_i`
So to calculate the average of several values, we add all the values and divide the result by the number of values.
Using this formula, for example, we can calculate the quarterly average for a student who got 13; 16; 7 and 12 on his math homework.
Weighted average
To calculate the weighted average of a statistical series defined by giving the pairs `(x_i;n_i)`, where `x_i` is the value of the characteristic under study and `n_i` is the number of that value, `i in NN`, `1<=i<=p`, we use the formula : `bar x= (sum_(i=1)^n x_i*n_i)/(sum_(i=1)^n n_i)=(n_1*x_1+n_2*x_2+...+x_p)/(n_1+n_2+...+n_p)`
Using this formula, it is for example possible to calculate the weighted average of a student who got 16 in French (coefficient 3), 11 in English (coefficient 2), 12 in mathematics (coefficient 5).
The frequency
The frequency of a data is the quotient obtained by dividing the number of this data by the total number.
F=`"number"/"total number"`