How do you find the mean, median, and mode of the following frequency distribution table?

Score* (Number of Students) 10 - 6 9 - 13 8 - 12 7 - 11 6 - 13 5 - 5

Aug 6, 2018

$\text{Mean "bar(X)=67.55 ," Median " M=8 and "Mode } Z = 13$

Explanation:

Let us ordering the data from least to greatest.

Please see the table given below.

Let ,

${x}_{i} = \text{Score" and f_i="Number of students}$

$N = \text{Total Number of students}$

$\mathmr{and} C {f}_{i} = \text{Comulative frequency}$ color(red)((1)"Mean " bar(X)=(sum f_ix_i)/N =(453)/60=67.55

$\text{Median " M=((N+1)/2)th " score} \to {x}_{i}$

$\text{Median " M=((60+1)/2)th " score} \to {x}_{i}$

$\text{Median " M=((30.5)th " score} \to {x}_{i}$

Now ,from $C {f}_{i} \to 29 < 30.5 , \mathmr{and} 30.5 > 41$

So, see the cell in the green color :

color(green)(Cf_i=41to "for "x_i=8

$\therefore \text{Median } M = 8$

$\left(3\right) \text{ Mode " Z="Frequency repeated in the set of data,}$
color(white)((3)" Mode " Z=)"maximum number of times"

:.color(orange)(" Mode " Z=13to"see the yellow color in table for "f_i.

$i . e . \text{ Mode } Z = 13$

Hence ,

$\text{Mean "bar(X)=67.55 ," Median " M=8 and "Mode } Z = 13$