Question

Caffeine: Following are the number of grams of carbohydrates in 12-ounce espresso beverages offered at a coffee shop.2319261716913131321362931332837384943404039464437(a) What is the 39th percentile?The 39th percentile is the data value(b) What is the 78th percentile?The 78th percentile is the data value

Answer 1

a) To find the 39th percentile:

1. Order all the values in the data set from smallest to largest:

`9,13,13,13,16,17,19,21,23,26,28,29,31,33,36,37,37,38,39,40,40,43,44,46,49`

2. Multiply 39% by the total number of values:

`(39)/(100)*25=9.75`

3. Round the number you get in previous step to the nearest whole number:

`9.75\approx10`

4. The data in the 10th position (ordered values) is the 39th percentile.

39th percentile: 26

The 39th percentile is the data value 26

b) To find the 78th percentile:

1. Use the ordered values you get above:

`9,13,13,13,16,17,19,21,23,26,28,29,31,33,36,37,37,38,39,40,40,43,44,46,49`

2. Multiply 78% by the total number of values:

`(78)/(100)*25=19.5`

3. Round the number you get in previous step to the nearest whole number:

`19.5\approx20`

4. The data in the 20th position (ordered values) is the 78th percentile.

78th percentile: 40

The 78th percentile is the data value 40