Mean, Median and Mode — Example 2
The owner of a new Indian restaurant is wondering how its prices compare with others in the local
area. Use the following price information on a sample of 16 rogan josh main dishes to write a short
report to the restaurant owner about the central tendency of the data.
Central Tendencies what we have to find are “Mean”, Median” and “Mode”
Mean:-
Mean = Sum(Prices) / Total Number of Restaurants
Mean = (14.5+13.9+10.9+13.5+12.9+14.5+13.9+11.5+14.9+14.5+11.9+11.5+11.5+14.5+12.5 +10.5) / 16
Mean = 207.4 / 16
Mean = 12.9625
Median:
List of prices = sort[14.5,13.9,10.9,13.5,12.9,14.5,13.9,11.5,14.9,14.5,11.9,11.5,11.5,14.5,12.5 ,10.5]
sorted list of prices = [10.5,10.9,11.5,11.5,11.5,11.9,12.5,12.9,13.5,13.9,13.9,14.5,14.5,14.5,14.5,14.9]
Median when Total count is even = average ((N/2)th position item + ((N/2+1)th position item)
Where N is Total Count of items in a tables
Median = average((16/2 th position item + (16+1)/2 th position item)
Median = (8th position item + 8.5th position item) / 2
After rounding off
Median = (8th position item + 9th position item) / 2
Median = (12.9 + 13.5) / 2
Median = 13.2
Mode:
Number if times each price is present
10.5–1 time
10.9–1 time
11.5–3 times
11.9–1 time
12.5–1 time
12.9–1 time
13.5–1 time
13.9–2 times
14.5–4 times
14.9–1 time
So, in this case 14.5 is the mode.
Inference:
1). If mean is the primary evaluation metric, then Indian restaurant owner can consider $12.96 as price for his rogan josh main dish.
2). If median is the primary evaluation metric, then Indian restaurant owner can consider $13.2 as price for his rogan josh main dish.
3). If mode is the primary evaluation metric, then Indian restaurant owner can consider $14.5 as price for his rogan josh main dish.
Deciding evaluation metric will depends on Indian Restaurant owner in this case.
Conclusion:
For any Data Science Problem, Inference is more important than calculation. While learning data science we would have concentrated more on formulas and calculation, but inference what we are getting from it is more important for business people to take decisions.
