Question

At an exchange, number of calls received in 245 successive one minute interval is given below. Determine the mean and the mode of the distribution?

No. of calls:  0,      1,      2,      3,      4,     5,     6,     7,    Total 

Frequency: 14,    21,    25,    43,    51    40    39    12    245 

Answer 1

Solution:

Mean (Weighted Arithmetic Mean) of a frequency distribution is given by the formula: 

x̅=∑xifi / ∑f_i = ∑xifi / N

 

Given frequency distribution of calls received:

 No. of calls, x_i:  0,      1,      2,      3,      4,      5,      6,     7,   Total 

Frequency, f_i: 14,    21,    25,    43,    51,     40,    39,  12    245 

Calculate   xifi:   0,    21,    50,   129,  204, 200, 234, 84,

 

N = 245 and ∑xifi = 0 + 21 + 50 +129 + 204 + 200 + 234 + 84 = 922

So, mean x̅= ∑xifi / N = 922 / 245 = 3.8

Mode is the value of x with maximum frequency.

Maximum frequency is 51 for x = 4. So, mode = 4

 

Thus, for the given distribution mean is 3.8 and mode is 4.

 

For the given distribution the mean is 3.8 and the mode is 4.