Mean and Median — Example 1

A Department store manager is interested in the number of complaints received by the customer service department about the quality of electrical products sold by the store. Records over a 10-week period yield the data shown in the table

(a) Fine the mean number of weekly complaints for this population.

(b) Find the median number of weekly complaints for this population.

Answer:

Population = N = 10

X1= 13, X2 = 15 …… X10 = 15

Mean =

Mean of weekly complaints = (13+15+8+16+8+4+21+11+3+15) / 10

Mean of weekly complaints = (114) / 10

Mean of weekly complaints = 11.4

Median = Central value of Sorted list

Median of weekly complaints = ?

Sorted list = [3, 4, 8, 8, 11, 13, 15, 15, 16, 21]

List as Dictionary = {1:3, 2:4, 3:8, 4:8, 5:11, 6:13, 7:15, 8:15, 9:16, 10:21]

To better identify the subscript when calculating the median.

If N is even, Average of ( ( N/2 ) + ( ( N+1 )/2 ) ) )

Applying in Formula

Median of weekly complaints = Average of (value at location (10/2) + (value at location (10+1)/2)))

Median of weekly complaints = Average of (value at location 5 + value at location 5.5)

Median of weekly complaints = Average of (value at location 5 + value at location 6)

Median of weekly complaints = Average of ( 11 + 13)

Median of weekly complaints = 24 / 2

Median of weekly complaints = 12

a). Mean of weekly complaints = 11.4

b). Median of weekly complaints = 12

Median is greater than mean, so we can say it is slightly left skewed data.

Instead of learning theory, Solving problems and understanding from it is a better method i felt. So trying to solve problems and i will try to post more problems in medium.

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