The link that you have provided gives information for each year in the 1950s and 1960s. I have chosen 1955 and 1965 as representative years from each “period” and I am using the data from those years.
First, let us look at the data. There were five items for which there were prices given in both 1955 and 1965. Those were a gallon of milk, a loaf of bread, a gallon of gas, a new car, and a new house. The price of milk went from $.92 in 1955 to $1.05 in 1965. The price of bread went from 18 cents to 21 cents. The price of gas went from 23 cents to 24 cents. The price of a car went from $1950 to $2350. The price of a house went from $22,000 to $40,000.
To compute the change in the cost of living, we want to find out the percent change from 1955 to 1965. The formula is (1965 price – 1955 price) divided by 1955 price. When we do the math, we see that milk increased by 14%, bread by 17%, gas by 4%, cars by 20% and houses by a whopping 82%.
So what does that tell us about the overall increase in the cost of living? You could just add up the prices of everything and determine the percent change for the whole “basket” of goods. That would tell us that the cost of living went up 77% in 10 years, which is a tremendous jump. The problem is that this is skewed by the huge difference in the cost of cars and houses (which you don’t have to buy often) and the price of the other things, which you do have to buy often.
I would use the prices of the milk, bread, and gas only. I would conclude from those prices that the cost of living increased by about 13% over these years.