find th median for the given frequency distribution: class40_45 frequency2 45_50 3 50_55 8 55_60 6 60_65 6 65_70 3 70_75 2
Answers
Step-by-step explanation:
Median = 56.67 or approx 57.
Step-by-step explanation:
We are given the following frequency distribution below;
Classes Frequency (f) Cumulative frequency (cf)
40 - 45 2 2
45 - 50 3 5
50 - 55 8 13
55 - 60 6 19
60 - 65 6 25
65 - 70 3 28
70 - 75 2 30
\sum f∑f = 30
Firstly, we will calculate \frac{N}{2}
2
N
, (where N = ∑f), \frac{N}{2}
2
N
= \frac{30}{2}
2
30
= 15.
So, the value of cumulative frequency just greater than or equal to 15 is 19.
Therefore, median class is 55 - 60 .
Now, Median formula = x_L + \frac{\frac{N}{2} -cf}{f_m} \times cx
L
+
f
m
2
N
−cf
×c
where, x_Lx
L
= lower limit of median class = 55
N = \sum f∑f = 30
f_mf
m
= frequency of median class = 6
cf = cumulative frequency just above the median class = 13
c = width of class interval = 5
So, Median = 55 + \frac{\frac{30}{2} -13}{6} \times 555+
6
2
30
−13
×5
= 55+\frac{10}{6}55+
6
10
= 55 + 1.67 = 56.67 or close to 57
Therefore, Median of given distribution is approx 57 .
Answer:
70+78×7=889 ki and we hope you're feeling