Q. 195.0( 1 Vote )

# Find the mean, median and mode of the following data:

Answer :

For equal class intervals, we will solve by finding mid points of these classes using direct method.

We have got

Σf_{i} = 50 and Σf_{i}x_{i} = 1500

∵ mean is given by

⇒

⇒

Thus, mean is 30.

To find median, Assume

Σf_{i} = N = Sum of frequencies,

h = length of median class,

l = lower boundary of the median class,

f = frequency of median class

and C_{f} = cumulative frequency

Lets form a table.

We have got

So, N = 50

⇒ N/2 = 50/2 = 25

The cumulative frequency just greater than (N/2 = ) 25 is 39, so the corresponding median class is 30 - 40 and accordingly we get C_{f} = 24(cumulative frequency before the median class).

Now, since median class is 30 - 40.

∴ l = 30, h = 10, f = 15, N/2 = 25 and C_{f} = 24

Median is given by,

⇒

= 30 + 0.67

= 30.67

Thus, median is 30.67.

Since, we have got mean = 30 and median = 30.67

Applying the empirical formula,

Mode = 3(Median) – 2(Mean)

⇒ Mode = 3(30.67) – 2(30)

⇒ Mode = 92.01 – 60 = 32.01

∴ Mean = 30, Median = 30.67 and Mode = 32.01

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