Question

value of x and y if median is 58 and sum of frequencies is 140​

Answer 1

Answer

x = 15, y = 20

Solution

We know that, median = $\sf l + \frac{\frac{n}{2} - cf}{f} \times h$

Where, l = lower limit of medial class

n/2 = Half of sum of frequencies

cf = cumulative frequency of class preceding medial class

f = frequency of medial class

and h = class size

Here,

l = 55 (since 58 lies between 55 - 65, medial class would be 55 - 65)

n = 140

→ n/2 = 70

cf = 8 + 10 + x + 25 = 43 + x

f = 40

h = 10

and median = 58

So, applying the formula we get,

$\sf 55 + \frac{70 - 43 - x}{40} \times 10 = 58$

$\sf \frac{27 - x}{4} = 58 - 55$

$\sf 27 - x = 4 \times 3$

27 - x = 12

→ x = 15

Now, sum of frequencies = 140

→ 8 + 10 + x + 25 + 40 + y + 15 + 7 = 140

→ 105 + x + y = 140

→ 105 + 15 + y = 140

→ y = 20

Answer 2

Answer:

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