Answer to Question #215097 in Statistics and Probability for Lata

Question

Draw the cumulative frequency curve for the data given below
Marks: 0-10 10-20 20-30 30-40
No of students: 4 8 11 15
40-50 50-60 60-70
12 6 3

Answer 1

The total number of students: $N=4+8+11+15+12+6+3=59$

Therefore, the corresponding partial frequencies (x_i) are 4/59, 8/59, 11/59, 15/59, 12/59, 6/59, 3/59

The accumulated relative frequencies can be found by summarizing $S_i=x_1+\dots +x_i$ or by the formula $S_{i}=S_{i-1}+x_i$.

$S_1=4/59$, $S_2=(4+8)/59=12/59$, $S_3=(12+11)/59=23/59$, $S_4=(23+15)/59=38/59$, $S_5=(38+12)/59=50/59$, $S_6=(50+6)/69=56/59$,

$S_7=(56+3)/59=1$

Put the obtained midpoints of the intervals, relative frequencies and accumulated relative frequencies into the table:

Draw the cumulative frequency curve: