## 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

Question

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

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2 weeks 2021-10-01T21:24:37+00:00 2 Answers 0 views 0

1. 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 .