In: Math
AM -vs- PM Test Scores: In my AM section of statistics there are 22 students. The scores of Test 1 are given in the table below. The results are ordered lowest to highest to aid in answering the following questions.
index | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 |
score | 35 | 50 | 58 | 59 | 60 | 61 | 65 | 66 | 68 | 68 | 71 | 74 | 76 | 76 | 79 | 82 | 84 | 88 | 90 | 92 | 94 | 97 |
(a) The value of P90 ---->
(b) Complete the 5-number summary.
Minimum | = | 35 |
Q1 | = | ??? |
Q2 | = | ??? |
Q3 | = | ??? |
Maximum | = | 97 |
First the data has to be arranged in the ascending order which the data is already arranged.
a) Percentile divides the data into 100 parts.
The formula to look for the k th percentile value =
n = 22
= 92 + 0.7 (94 - 92)
= 93.4
(b) Complete the 5-number summary.
Minimum | = | 35 |
Q1 | = | ![]() |
Q2 | = | ![]() |
Q3 | = | ![]() |
Maximum | = | 97 |
Quartile divides the data into 4 parts.
= 5th + 0.75 (6th - 5th) value
= 60 + 0.75 (61 - 60)
= 60.75
= 11th + 0.5 (12th -11th) value
= 71 + 0.5 (74 - 71)
= 72.5
= 17th + 0.25 (18th -17th) value
= 84 + 0.25 (88 - 84)
= 85